{"id":147,"date":"2023-11-08T16:10:06","date_gmt":"2023-11-08T16:10:06","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/chapter\/read-multiply-polynomials\/"},"modified":"2026-02-05T10:24:40","modified_gmt":"2026-02-05T10:24:40","slug":"3-1-review-properties-of-exponents-and-intro-to-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/chapter\/3-1-review-properties-of-exponents-and-intro-to-polynomials\/","title":{"raw":"3.1 Review: Properties of Exponents and Intro to Polynomials","rendered":"3.1 Review: Properties of Exponents and Intro to Polynomials"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Simplify expressions by applying the Properties of Exponents<\/li>\r\n \t<li>Multiply polynomials<\/li>\r\n<\/ul>\r\n<\/div>\r\nA common language is needed in order to communicate mathematical ideas clearly and efficiently. <strong>Exponential notation<\/strong>\u00a0was developed to write repeated multiplication more efficiently. For example, growth occurs in living organisms by the division of cells. One type of cell divides\u00a0[latex]2[\/latex] times in an hour. So in\u00a0[latex]12[\/latex] hours, the cell will divide [latex]\\overbrace{2\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}}^{2^{12}}[\/latex] times.\u00a0This can be expressed\u00a0more efficiently as [latex]2^{12}[\/latex]. In this section we will learn how to simplify and perform mathematical operations such as multiplication and division on terms that have exponents.\r\n<h2>Exponential Expressions<\/h2>\r\nWe use exponential notation to write repeated multiplication. For example, [latex]10\\cdot10\\cdot10[\/latex] can be written more succinctly as [latex]10^{3}[\/latex]. The\u00a0[latex]10[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>base<\/b>. The\u00a0[latex]3[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>exponent<\/b>. The expression [latex]10^{3}[\/latex] is called the exponential expression. Knowing the names for the parts of an exponential expression will help you learn how to perform mathematical operations on them.\r\n<p style=\"text-align: center;\">[latex]\\text{base}\\rightarrow10^{3\\leftarrow\\text{exponent}}[\/latex]<\/p>\r\n[latex]10^{3}[\/latex] is read as \u201c[latex]10[\/latex] to the third power\u201d or \u201c[latex]10[\/latex] cubed.\u201d It means [latex]10\\cdot10\\cdot10[\/latex], or [latex]1,000[\/latex].\r\n\r\n[latex]8^{2}[\/latex]\u00a0is read as \u201c[latex]8[\/latex] to the second power\u201d or \u201c[latex]8[\/latex] squared.\u201d It means [latex]8\\cdot8[\/latex], or [latex]64[\/latex].\r\n\r\n[latex]5^{4}[\/latex]\u00a0is read as \u201c[latex]5[\/latex] to the fourth power.\u201d It means [latex]5\\cdot5\\cdot5\\cdot5[\/latex], or\u00a0[latex]625[\/latex].\r\n\r\n[latex]b^{5}[\/latex]\u00a0is read as \u201c[latex]b[\/latex] to the fifth power.\u201d It means [latex]{b}\\cdot{b}\\cdot{b}\\cdot{b}\\cdot{b}[\/latex]. Its value will depend on the value of [latex]b[\/latex].\r\n\r\nThe exponent applies only to the number or the variable that it is attached to. Therefore, in the expression [latex]xy^{4}[\/latex],\u00a0only the [latex]y[\/latex] is affected by the\u00a0[latex]4[\/latex]. [latex]xy^{4}[\/latex]\u00a0means [latex]{x}\\cdot{y}\\cdot{y}\\cdot{y}\\cdot{y}[\/latex]. The [latex]x[\/latex] is <strong>not<\/strong> being raised to the 4th power.\r\n\r\nConsider an expression like [latex]\u22123^{4}[\/latex]. In the previous paragraph, <strong>only<\/strong> the [latex]3[\/latex] is being raised to the 4th power (not the negative). You can rewrite the expression as [latex]-1\\cdot3^{4}[\/latex] which means [latex]\u20131\\cdot\\left(3\\cdot3\\cdot3\\cdot3\\right)[\/latex], or [latex]\u221281[\/latex].\r\n\r\nIf [latex]\u22123[\/latex] is to be the base, it must be written using parentheses as [latex]\\left(\u22123\\right)^{4}[\/latex], which means [latex](\u22123)\\cdot(\u22123)\\cdot(\u22123)\\cdot(\u22123)[\/latex], or\u00a0[latex]81[\/latex].\r\n\r\nLikewise,\u00a0[latex]\\left(\u2212x\\right)^{4}=\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)=x^{4}[\/latex], while [latex]\u2212x^{4}=\\ \u20131\\cdot\\left(x\\cdot x\\cdot x\\cdot x\\right)[\/latex].\r\n<p class=\"no-indent\">In the following video, you are provided more examples of applying exponents to various bases.<\/p>\r\nhttps:\/\/youtu.be\/ocedY91LHKU\r\n<div class=\"textbox shaded\">\r\n\r\n<img class=\"alignleft wp-image-2132\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01182614\/traffic-sign-160659-300x265.png\" alt=\"Caution Sign\" width=\"75\" height=\"66\" \/>Caution! Whether to include a negative sign as part of a base or not often leads to confusion. To clarify\u00a0whether a negative sign is applied before or after the exponent, here is an example.\r\n\r\nWhat is the difference in the way you would evaluate these two terms?\r\n<ol>\r\n \t<li style=\"text-align: left;\">[latex]-{3}^{2}[\/latex]<\/li>\r\n \t<li style=\"text-align: left;\">[latex]{\\left(-3\\right)}^{2}[\/latex]<\/li>\r\n<\/ol>\r\nTo evaluate 1), you would apply the exponent to the three first, then apply the negative sign last, like this:\r\n<p style=\"text-align: center;\">[latex]\\begin{align}&amp;\\quad\\,-3^2\\\\ &amp;=-\\left({3}^{2}\\right)&amp;\\\\ &amp;=-\\left(9\\right) &amp;\\\\ &amp;= -9\\end{align}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">To evaluate 2), you would apply the exponent to the negative [latex]3[\/latex]:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{align}&amp;\\quad\\;\\left(-3\\right)^{2}&amp;\\\\ &amp;=\\left(-3\\right)\\cdot\\left(-3\\right)&amp;\\\\ &amp;={ 9}\\end{align}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">The key to remembering this is to follow the order of operations. The first expression does not include parentheses so you would apply the exponent to the integer [latex]3[\/latex] first, then apply the negative sign. The second expression includes parentheses, so hopefully you will remember that the negative sign also gets squared.<\/p>\r\n\r\n<\/div>\r\n<h2><\/h2>\r\n<h2>Properties of Exponents<\/h2>\r\nHere is an overview of the properties of exponents. For a more detailed explanation and examples of these properties, please click on the property in the table you would like to review to or scroll down to corresponding section below.\r\n\r\nIf you do not need to review the properties of exponents, you can skip down the page to <a class=\"anchorLink\" href=\"#pf\">Polynomial Functions and Expressions<\/a> where you can review adding, subtracting, and multiplying polynomial expressions and also review evaluating polynomial functions.\r\n<table style=\"width: 70%;\"><caption style=\"caption-side: top; font-size: large;\">Properties of Exponents\r\n<em>Assume denominators do not equal zero and [latex]m[\/latex] and [latex]n[\/latex] represent integers<\/em><\/caption>\r\n<thead>\r\n<tr>\r\n<th>\u00a0Name<\/th>\r\n<th>Property<\/th>\r\n<th>Example<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#product\">Product Rule<\/a><\/td>\r\n<td>[latex]{\\large a^{m}\\cdot{a}^{n}=a^{m+n}}[\/latex]<\/td>\r\n<td>[latex]{\\large x^{3}\\cdot{x}^{2}=x^{3+2}=x^5}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#quotient\">Quotient Rule<\/a><\/td>\r\n<td>[latex]{\\large \\dfrac{a^{m}}{{a}^{n}}=a^{m-n}}[\/latex]<\/td>\r\n<td>[latex]{\\large \\dfrac{x^{7}}{{x}^{4}}=x^{7-4}=x^3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#power\">Power Rule<\/a><\/td>\r\n<td>[latex]{\\large \\left(a^{m}\\right)^{n}=a^{m\\cdot{n}}}[\/latex]<\/td>\r\n<td>[latex]{\\large \\left(x^{2}\\right)^{4}=x^{2\\cdot{4}}=x^8}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#p of p\">Power of a Product Rule<\/a><\/td>\r\n<td>[latex]{\\large \\left(ab\\right)^{n}=a^{n}\\cdot b^{n}}[\/latex]<\/td>\r\n<td>[latex]{\\large \\left(2y\\right)^{3}=2^{3}\\cdot y^{3}=8y^3}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#p of q\">Power of a Quotient Rule<\/a><\/td>\r\n<td>[latex]{\\large \\left(\\dfrac{a}{b}\\right)^{n}=\\dfrac{{a}^{n}}{{b}^{n}}, b \\ne{0}}[\/latex]<\/td>\r\n<td>[latex]{\\large \\left(\\dfrac{x}{3}\\right)^{2}=\\dfrac{{x}^{2}}{{3}^{2}}=\\dfrac{x^2}{9}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#zero\">Zero Exponent Rule<\/a><\/td>\r\n<td>[latex]{\\large \\left({a}\\right)^{0}=1,{a} \\ne{0}}[\/latex]<\/td>\r\n<td>[latex]{\\large \\left({-4x^5}\\right)^{0}=1}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><a class=\"anchorLink\" href=\"#negative\">Negative Exponent Rule<\/a><\/td>\r\n<td><span style=\"background-color: #ffffff;\">[latex]{\\large {a}^{-n}=\\dfrac{1}{{a}^{n}}, {a} \\ne{0}}[\/latex]<\/span><\/td>\r\n<td>[latex]{\\large {x}^{-4}=\\dfrac{1}{{x}^{4}}}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2><\/h2>\r\n<h2 id=\"product\">Product Rule to Multiply Exponential Expressions<\/h2>\r\nWhat happens if you multiply two numbers in exponential form with the same base? Consider the expression [latex]{2}^{3}{2}^{4}[\/latex]. Exponents are repeated multiplication so we can Expand each exponent as [latex]\\left(2\\cdot2\\cdot2\\right)\\left(2\\cdot2\\cdot2\\cdot2\\right)[\/latex] or [latex]2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2[\/latex]. In exponential form, you would write the product as [latex]2^{7}[\/latex]. Notice that [latex]7[\/latex] is the sum of the original two exponents,\u00a0[latex]3[\/latex] and\u00a0[latex]4[\/latex].\r\n\r\nWhat about [latex]{x}^{2}{x}^{6}[\/latex]? This can be written as [latex]\\left(x\\cdot{x}\\right)\\left(x\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\right)=x\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}[\/latex] or [latex]x^{8}[\/latex]. And, once again, [latex]8[\/latex] is the sum of the original two exponents. This concept can be generalized in the following way:\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Product Rule for Exponents<\/h3>\r\nFor any number [latex] a[\/latex] and any integers [latex]m[\/latex] and [latex]n[\/latex],\r\n\r\n[latex]\\left(a^{m}\\right)\\left(a^{n}\\right) = a^{m+n}[\/latex].\r\n\r\nIf [latex]m[\/latex], [latex]n[\/latex], or [latex]m+n[\/latex] is [latex]0[\/latex] or negative, then [latex]a[\/latex] cannot be [latex]0[\/latex].\r\n\r\nTo multiply exponential expressions with the same base, add the exponents.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWrite each of the following products with a single base. Do not simplify further.\r\n<ol>\r\n \t<li>[latex]{t}^{5}\\cdot {t}^{3}[\/latex]<\/li>\r\n \t<li>[latex]{-3x^2}\\cdot {4x^5}[\/latex]<\/li>\r\n \t<li>[latex]{x}^{2}\\cdot {x}^{5}\\cdot {x}^{3}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"772709\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"772709\"]\r\n\r\nUse the product rule to simplify each expression.\r\n<ol>\r\n \t<li>[latex]{t}^{5}\\cdot {t}^{3}={t}^{5+3}={t}^{8}[\/latex]<\/li>\r\n \t<li>[latex]{-3x^2}\\cdot {4x^5}={-3}\\cdot {4}\\cdot{x}^{2+5}=-12x^7[\/latex]<\/li>\r\n \t<li>[latex]{x}^{2}\\cdot {x}^{5}\\cdot {x}^{3}={x}^{2+5+3}={x}^{10}[\/latex]<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div style=\"text-align: center;\">[\/hidden-answer]<\/div>\r\n&nbsp;\r\n\r\nIn the following video, you will see more examples of using the product rule for exponents to simplify expressions.\r\nhttps:\/\/youtu.be\/P0UVIMy2nuI\r\n<h2 id=\"quotient\">Quotient Rule to Divide Exponential Expressions<\/h2>\r\nLet us look at dividing terms containing exponential expressions. What happens if you divide two numbers in exponential form with the same base? Consider the following expression: [latex]\\dfrac{7^5}{7^2}[\/latex]. You can rewrite the expression as [latex]\\dfrac{7\\cdot 7\\cdot 7\\cdot 7\\cdot 7}{7\\cdot 7}[\/latex].\r\n\r\nThen you can divide out the common factors of 7 in the numerator and denominator:\r\n\r\n[latex]\\require{color}\\dfrac{\\color{red}\\cancel{\\color{black}7} \\color{black} \\cdot \\color{red}\\cancel{\\color{black}7} \\color{black} \\cdot 7 \\cdot 7 \\cdot 7}{\\color{red}\\cancel{\\color{black}7} \\color{black} \\cdot \\color{red}\\cancel{\\color{black}7 \\color{black}}}[\/latex]\r\n<h2><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Finally, this expression can be rewritten as [latex]7^{3}[\/latex]\u00a0using exponential notation. Notice that the exponent,\u00a0[latex]3[\/latex], is the difference between the two exponents in the original expression,\u00a0[latex]5[\/latex] and\u00a0[latex]2[\/latex]. So,\u00a0[latex] \\dfrac{7^5}{7^2}=7^{5-2}=7^{3}[\/latex].<\/span><\/h2>\r\n<h2><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Be careful that you subtract the exponent in the denominator from the exponent in the numerator. So, to divide two exponential expressions with the same base, subtract the exponents.<\/span><\/h2>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Quotient (Division) Rule for Exponents<\/h3>\r\nFor any non-zero number [latex]a[\/latex] and any integers [latex]m[\/latex] and [latex]n[\/latex]:\r\n\r\n[latex] \\displaystyle \\dfrac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}, a \\ne 0[\/latex]\r\n\r\nTo divide exponential expressions with the same base, subtract the exponents.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3><span style=\"font-size: 1em;\">Example<\/span><\/h3>\r\nWrite each of the following products with a single base. Do not simplify further.\r\n<ol>\r\n \t<li>[latex]\\dfrac{{\\left(-2\\right)}^{14}}{{\\left(-2\\right)}^{9}}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{t}^{23}}{{t}^{15}}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"978732\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"978732\"]\r\n\r\nUse the quotient rule to simplify each expression.\r\n<ol>\r\n \t<li>[latex]\\dfrac{{\\left(-2\\right)}^{14}}{{\\left(-2\\right)}^{9}}={\\left(-2\\right)}^{14 - 9}={\\left(-2\\right)}^{5}=(-2)\\cdot(-2)\\cdot(-2)\\cdot(-2)\\cdot(-2) = -32[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{t}^{23}}{{t}^{15}}={t}^{23 - 15}={t}^{8}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<span style=\"color: #000000;\">In the following video, you will see more examples of using the quotient rule for exponents.<\/span>\r\n\r\nhttps:\/\/youtu.be\/xy6WW7y_GcU\r\n<h2 id=\"power\">Raise Exponential Expressions to Powers<\/h2>\r\nAnother word for exponent is power. You have likely seen or heard an example such as [latex]3^5[\/latex] can be described as\u00a0[latex]3[\/latex] raised to the\u00a0[latex]5[\/latex]th power. In this section we will further expand our capabilities with exponents. We will learn what to do when an expression with a\u00a0power\u00a0is raised to another power and what to do when two numbers or variables are multiplied and both are raised to a power. We will also learn what to do when numbers or variables that are divided are raised to a power. We will begin by raising exponential expressions to powers.\r\n\r\nLet us simplify [latex]\\left(5^{2}\\right)^{4}[\/latex].\r\n\r\nIn this case, [latex]\\left(5^{2}\\right)^{4}[\/latex] indicates that the quantity [latex]5^2[\/latex]<sup>\u00a0<\/sup>is raised to the fourth power , so you multiply [latex]5^{2}[\/latex]<sup>\u00a0<\/sup>four times: [latex]\\left(5^{2}\\right)^{4}=5^{2}\\cdot5^{2}\\cdot5^{2}\\cdot5^{2}=5^{8}[\/latex]<sup>\u00a0<\/sup>(using the Product Rule\u2014add the exponents).\r\n\r\nWe saw above that the answer is [latex]5^{8}[\/latex]. Notice that the new exponent is the same as the product of the original exponents: [latex]2\\cdot4=8[\/latex]. So, [latex]\\left(5^{2}\\right)^{4}=5^{2\\cdot4}=5^{8}[\/latex]\u00a0(which equals [latex]390,625[\/latex] if you do the multiplication).\r\n\r\nLikewise, [latex]\\left(x^{4}\\right)^{3}=x^{4\\cdot3}=x^{12}[\/latex].\r\n\r\nThis leads to the <b>Power Rule for Exponents<\/b>. To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, [latex]\\left(2^{3}\\right)^{5}=2^{15}[\/latex].\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Power Rule for Exponents<\/h3>\r\nFor any real number [latex]a[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]:\r\n\r\n[latex]\\left(a^{m}\\right)^{n}=a^{m\\cdot{n}}[\/latex].\r\n\r\nIf [latex]m[\/latex] or [latex]n[\/latex] is [latex]0[\/latex] or negative, then [latex]a[\/latex] must not be [latex]0[\/latex].\r\n\r\nWhen raising an exponential expression to a power, keep the base the same and multiply the exponents.\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<em>Take a moment to contrast in your mind <strong>how the power rule for exponents is different from the product rule for exponents. <\/strong>With the power rule you are multiplying the exponents but with the product rule you are adding the exponents.<\/em>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWrite each of the following products with a single base. Do not simplify further.\r\n<ol>\r\n \t<li>[latex]{\\left({x}^{2}\\right)}^{7}[\/latex]<\/li>\r\n \t<li>[latex]{\\left({\\left(-3\\right)}^{5}\\right)}^{11}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"841688\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"841688\"]\r\n\r\nUse the power rule to simplify each expression.\r\n<ol>\r\n \t<li>[latex]{\\left({x}^{2}\\right)}^{7}={x}^{2\\cdot 7}={x}^{14}[\/latex]<\/li>\r\n \t<li>[latex]{\\left({\\left(-3\\right)}^{5}\\right)}^{11}={\\left(-3\\right)}^{5\\cdot 11}={\\left(-3\\right)}^{55}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn the following video, you will see more examples of using the power rule to simplify expressions with exponents.\r\n\r\nhttps:\/\/youtu.be\/VjcKU5rA7F8\r\n\r\nBe careful to distinguish between uses of the <strong>product rule<\/strong> and the <strong>power rule<\/strong>.\r\n<ul>\r\n \t<li>Using the <strong>product rule:<\/strong>\u00a0When multiplying expressions with exponents with the same base, keep the base, add the exponents.<\/li>\r\n \t<li>Using the <strong>power rule:<\/strong>\u00a0When raising an expression with an exponent to a power, keep the base and multiply the exponents.<\/li>\r\n<\/ul>\r\n<h2 id=\"zero\">Zero Exponent Rule<\/h2>\r\nAbove when we used the quotient rule we had expressions for which [latex]m[\/latex] is larger than [latex]n[\/latex] so that the difference [latex]m-n[\/latex] would never be zero or negative.\r\n\r\nWhat would happen if [latex]m[\/latex] and [latex]n[\/latex] were equal? In this case, we would use the <em>zero exponent rule of exponents<\/em> to simplify the expression to\u00a0[latex]1[\/latex]. To see how this is done, let us begin with an<span style=\"background-color: #ffffff;\"> example<\/span>.\r\n\r\n[latex]\\require{color}\\dfrac{t^8}{t^8}=\\dfrac{\\color{red}\\cancel{\\color{black}{t^8}}}{\\color{red}\\cancel{\\color{black}{t^8}}}=1[\/latex]\r\n\r\nIf we were to simplify the original expression using the quotient rule, we would have: [latex]\\dfrac{{t}^{8}}{{t}^{8}}={t}^{8 - 8}={t}^{0}[\/latex]\r\n\r\nFor both methods of simplifying to be true, then [latex]{t}^{0}=1[\/latex]. This is true for any nonzero real number, or any variable representing a nonzero real number. The sole exception is the expression [latex]{0}^{0}[\/latex]. This appears later in more advanced courses, but for now, we will consider the value to be indeterminate.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Zero Exponent Rule for Exponents<\/h3>\r\nFor any nonzero real number [latex]a[\/latex], the zero exponent rule of exponents states that\r\n<div style=\"text-align: center;\">[latex]\\large{{a}^{0}=1}[\/latex]<\/div>\r\nAny number (except [latex]0[\/latex]) raised to the zero power is [latex]1[\/latex].\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify each expression using the zero exponent rule of exponents.\r\n<ol>\r\n \t<li>[latex]-3^2\\cdot{(-5x^2)}^{0}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{-3{x}^{5}}{{x}^{5}}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"375469\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"375469\"]\r\n\r\nUse the zero exponent and other rules to simplify each expression.\r\n\r\n1.\r\n\r\n[latex]\\begin{align}-3^2\\cdot{(-5x^2)}^{0} &amp;=-(3\\cdot 3)\\cdot 1 &amp;&amp; \\color{blue}{\\textsf{simplify exponents}}\\\\ &amp;= -(9)\\cdot1 &amp;&amp; \\color{blue}{\\textsf{multiply}}\\\\ &amp;=-9\\end{align}[\/latex]\r\n\r\n2.\r\n\r\n[latex]\\begin{align}\\dfrac{-3{x}^{5}}{{x}^{5}} &amp;= -3\\cdot \\dfrac{{x}^{5}}{{x}^{5}}\\\\ &amp;= -3\\cdot {x}^{5 - 5}\\\\ &amp;= -3\\cdot {x}^{0} &amp;&amp; \\color{blue}{\\textsf{subtract exponents}}\\\\ &amp;= -3\\cdot 1 &amp;&amp; \\color{blue}{\\textsf{multiply}}\\\\ &amp;= -3 \\end{align}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn the following video, you will see more examples of simplifying expressions whose exponents may be zero.\r\n\r\nhttps:\/\/youtu.be\/rpoUg32utlc\r\n<h2 id=\"negative\">Negative Exponent Rule<\/h2>\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Can we simplify [latex]\\dfrac{{h}^{3}}{{h}^{5}}[\/latex]? <\/span><\/h3>\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">When [latex]n\\ is\\ larger\\ than\\ m[\/latex], the difference [latex]m-n[\/latex] is negative. We can use the <\/span><em style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">negative rule of exponents<\/em><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\"> to simplify the expression so that it is easier to understand. <\/span><\/h3>\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Let's look at an example to clarify this idea. Given the expression:\u00a0<\/span><span style=\"color: #373d3f; font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2;\">[latex]\\dfrac{{h}^{3}}{{h}^{5}}[\/latex].\u00a0<\/span><\/h3>\r\nLet's expand the numerator and denominator and then divide out the common factors to simplify.\r\n\r\n[latex]\r\n\\begin{align}\r\n\\dfrac{h^3}{h^5} &amp;= \\dfrac{h\\cdot h\\cdot h}{h\\cdot h\\cdot h\\cdot h\\cdot h}\\\\\r\n&amp;= \\dfrac{{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}}\r\n{{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}\\cdot h\\cdot h}\\\\\r\n&amp;= \\dfrac{1}{h\\cdot h}\\\\\r\n&amp;= \\dfrac{1}{h^2}\r\n\\end{align}\r\n[\/latex]\r\n\r\nOr, we can simplify using the Quotient Rule:\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">[latex]\\begin{array}{ccc}\\hfill \\dfrac{{h}^{3}}{{h}^{5}}&amp; =&amp; {h}^{3 - 5}\\hfill \\\\ &amp; =&amp; \\text{ }{h}^{-2}\\hfill \\end{array}[\/latex]<\/span><\/h3>\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Putting the answers together, we have [latex]{h}^{-2}=\\dfrac{1}{{h}^{2}}[\/latex]. This is true for any nonzero real number, or any variable representing a nonzero real number.<\/span><\/h3>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Negative Rule of Exponents<\/h3>\r\nFor any nonzero real number [latex]a[\/latex] and any integer [latex]n[\/latex], the negative rule of exponents states that\r\n<div style=\"text-align: center;\">[latex]\\large{{a}^{-n}=\\dfrac{1}{{a}^{n}}} , a\\ne 0[\/latex]<\/div>\r\n<div><\/div>\r\nWhen the exponent is negative, write the reciprocal of the base raised to the positive exponent.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify. Write answers with positive exponents.\r\n<ol>\r\n \t<li>[latex]\\dfrac{y^3}{{y}^{-4}}[\/latex]<\/li>\r\n \t<li>[latex]{-3}^{-2}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{(2b) }^{3}}{{(2b) }^{7}}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{z}^{2}\\cdot z}{{z}^{4}}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{\\left(-5{t}^{3}\\right)}^{4}}{{\\left(-5{t}^{3}\\right)}^{7}}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"552758\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"552758\"]\r\n<ol>\r\n \t<li>[latex]\\dfrac{y^3}{{y}^{-4}}=y^3 \\cdot y^4=y^7[\/latex]<\/li>\r\n \t<li>[latex]{-3}^{-2}= -1\\cdot {3}^{-2}=\\dfrac{-1}{3^2}=\\dfrac{-1}{3\\cdot 3}=\\dfrac{-1}{9}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{(2b) }^{3}}{{(2b)}^{7}}={(2b)}^{3 - 7}={(2b) }^{-4}=\\dfrac{1}{{(2b)}^{4}}=\\dfrac{1}{2^4 \\cdot {b}^{4}}=\\dfrac{1}{16b^4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{z}^{2}\\cdot z}{{z}^{4}}=\\dfrac{{z}^{2+1}}{{z}^{4}}=\\dfrac{{z}^{3}}{{z}^{4}}={z}^{3 - 4}={z}^{-1}=\\dfrac{1}{z}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{{\\left(-5{t}^{3}\\right)}^{4}}{{\\left(-5{t}^{3}\\right)}^{7}}={\\left(-5{t}^{3}\\right)}^{4 - 7}={\\left(-5{t}^{3}\\right)}^{-3}=\\dfrac{1}{{\\left(-5{t}^{3}\\right)}^{3}}=\\dfrac{1}{(-5)^3 \\cdot {(t^3)}^{3}}=\\dfrac{1}{-125 t^9}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<span style=\"color: #000000;\">In the following video, you will see examples of simplifying expressions with negative exponents.<\/span>\r\n\r\nhttps:\/\/youtu.be\/Gssi4dBtAEI\r\n<h2>Combine Exponent Rules to Simplify Expressions<\/h2>\r\nNow we will combine the use of the product and quotient rules to simplify expressions whose terms may have negative or zero exponents.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nWrite each of the following products with a single base. Write answers with positive exponents.\r\n<ol>\r\n \t<li>[latex]{b}^{2}\\cdot {b}^{-8}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(-x\\right)}^{5}\\cdot {\\left(-x\\right)}^{-5}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{-7z}{{\\left(-7z\\right)}^{3}}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"163692\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"163692\"]\r\n<ol>\r\n \t<li>[latex]{b}^{2}\\cdot {b}^{-8}={b}^{2 - 8}={b}^{-6}=\\dfrac{1}{{b}^{6}}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(-x\\right)}^{5}\\cdot {\\left(-x\\right)}^{-5}={\\left(-x\\right)}^{5 - 5}={\\left(-x\\right)}^{0}=1[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{-7z}{{\\left(-7z\\right)}^{3}}=\\dfrac{{\\left(-7z\\right)}^{1}}{{\\left(-7z\\right)}^{3}}={\\left(-7z\\right)}^{1 - 3}={\\left(-7z\\right)}^{-2}=\\dfrac{1}{{\\left(-7z\\right)}^{2}}=\\dfrac{1}{(-7)^2 \\cdot z^2}=\\dfrac{1}{49z^2}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nThe following video shows more examples of how to combine the use of the product and quotient rules to simplify expressions whose terms may have negative or zero exponents.\r\n\r\nhttps:\/\/youtu.be\/EkvN5tcp4Cc\r\n<h2 id=\"p of p\">Finding the Power of a Product<\/h2>\r\nTo simplify the power of a product of two exponential expressions, we can use the <em>power of a product rule of exponents\u00a0<\/em>which breaks up the power of a product of factors into the product of the powers of the factors.\r\nFor instance, consider [latex]{\\left(pq\\right)}^{3}[\/latex].\r\n\r\nWe begin by using the associative and commutative properties of multiplication to regroup the factors.\r\n\r\n[latex]\\begin{array}{ccc}\\hfill {\\left(pq\\right)}^{3}&amp; =&amp; \\stackrel{3\\text{ factors}}{{\\left(pq\\right)\\cdot \\left(pq\\right)\\cdot \\left(pq\\right)}}\\hfill \\\\ &amp; =&amp; p\\cdot q\\cdot p\\cdot q\\cdot p\\cdot q\\hfill \\\\ &amp; =&amp; \\stackrel{3\\text{ factors}}{{p\\cdot p\\cdot p}}\\cdot \\stackrel{3\\text{ factors}}{{q\\cdot q\\cdot q}}\\hfill \\\\ &amp; =&amp; {p}^{3}\\cdot {q}^{3}\\hfill \\end{array}[\/latex]\r\n\r\nIn other words, [latex]{\\left(pq\\right)}^{3}={p}^{3}\\cdot {q}^{3}[\/latex].\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Power of a Product Rule for Exponents<\/h3>\r\nFor any real numbers [latex]a[\/latex] and [latex]b[\/latex] and any integer [latex]n[\/latex], the power of a product rule of exponents states that\r\n<div style=\"text-align: center;\">[latex]\\large{\\left(a \\cdot b\\right)}^{n}={a}^{n}\\cdot {b}^{n}[\/latex]<\/div>\r\n<div><\/div>\r\nIf [latex]n[\/latex] is [latex]0[\/latex] or negative, neither [latex]a[\/latex] nor [latex]b[\/latex] can be [latex]0[\/latex].\r\n\r\nWhen raising a product to a power, apply the exponent to each factor in the product. Then simplify the expression.\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify each of the following products as much as possible using the power of a product rule. Write answers with positive exponents.\r\n<ol>\r\n \t<li>[latex]{\\left(a{b}^{2}\\right)}^{3}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(-2{w}^{3}\\right)}^{3}[\/latex]<\/li>\r\n \t<li>[latex]{\\left({j}^{3}{k}^{-2}\\right)}^{-4}[\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{{\\left(-2z\\right)}^{4}}[\/latex]<\/li>\r\n \t<li>[latex]{\\left({e}^{-2}{f}^{3}\\right)}^{7}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"788982\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"788982\"]\r\n\r\nUse the product and quotient rules and the new definitions to simplify each expression.\r\n<ol>\r\n \t<li>[latex]{\\left(a{b}^{2}\\right)}^{3}={\\left(a\\right)}^{3}\\cdot {\\left({b}^{2}\\right)}^{3}={a}^{1\\cdot 3}\\cdot {b}^{2\\cdot 3}={a}^{3}{b}^{6}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(-2{w}^{3}\\right)}^{3}={\\left(-2\\right)}^{3}\\cdot {\\left({w}^{3}\\right)}^{3}=-8\\cdot {w}^{3\\cdot 3}=-8{w}^{9}[\/latex]<\/li>\r\n \t<li>[latex]{\\left({j}^{3}{k}^{-2}\\right)}^{-4}=({j^3})^{-4} \\cdot ({{k}^{-2}})^{-4}={j}^{-12} \\cdot k^8=\\dfrac{k^8}{{j}^{12}} [\/latex]<\/li>\r\n \t<li>[latex]\\dfrac{1}{{\\left(-2z\\right)}^{4}}=\\dfrac{1}{{\\left(-2\\right)}^{4}\\cdot {\\left(z\\right)}^{4}}=\\dfrac{1}{16{z}^{4}}[\/latex]<\/li>\r\n \t<li>[latex]{\\left({e}^{-2}{f}^{3}\\right)}^{7}={\\left({e}^{-2}\\right)}^{7}\\cdot {\\left({f}^{3}\\right)}^{7}={e}^{-2\\cdot 7}\\cdot {f}^{3\\cdot 7}={e}^{-14}{f}^{21}=\\dfrac{{f}^{21}}{{e}^{14}}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3 style=\"text-align: center;\"><img class=\"alignleft wp-image-2132\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01183308\/traffic-sign-160659.png\" alt=\"Caution Sign.\" width=\"96\" height=\"83\" \/><\/h3>\r\n<div class=\"textbox shaded\">\r\n\r\nCaution! Do not try to apply this rule to sums.\r\n\r\nThink about the expression\u00a0[latex]\\left(2+3\\right)^{2}[\/latex]\r\n<p style=\"text-align: center;\">Does [latex]\\left(2+3\\right)^{2}[\/latex] equal [latex]2^{2}+3^{2}[\/latex]?<\/p>\r\nNo, it does not because of the order of operations!\r\n<p style=\"text-align: center;\">[latex]\\left(2+3\\right)^{2}=5^{2}=25[\/latex]<\/p>\r\n<p style=\"text-align: center;\">and<\/p>\r\n<p style=\"text-align: center;\">[latex]2^{2}+3^{2}=4+9=13[\/latex]<\/p>\r\nTherefore, you can only use this rule when the numbers inside the parentheses are being multiplied or divided.\r\n\r\n<\/div>\r\n<span style=\"color: #000000; font-size: 1rem; text-align: initial;\">In the following video, \u00a0we provide more examples of how to find the power of a product.<\/span>\r\n\r\nhttps:\/\/youtu.be\/p-2UkpJQWpo\r\n<h2 id=\"p of q\">Finding the Power of a Quotient<\/h2>\r\nTo simplify the power of a quotient of two expressions, we can use the <em>power of a quotient rule\u00a0<\/em>which states that the power of a quotient of factors is the quotient of the powers of the factors.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>The Power of a Quotient Rule of Exponents<\/h3>\r\nFor any real numbers [latex]a[\/latex] and [latex]b[\/latex] and any integer [latex]n[\/latex], the power of a quotient rule of exponents states that\r\n<div style=\"text-align: center;\">[latex]\\large{\\left(\\frac{a}{b}\\right)}^{n}=\\frac{{a}^{n}}{{b}^{n}}, b \\ne 0[\/latex]<\/div>\r\n<div><\/div>\r\nIf [latex]n[\/latex] is negative or [latex]0[\/latex], then [latex]a[\/latex] cannot be [latex]0[\/latex].\r\n\r\nWhen raising a quotient to a power, apply the exponent to the numerator and denominator. Then simplify the expression.\r\n\r\n<\/div>\r\n<div><\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify each of the following quotients as much as possible using the power of a quotient rule. Write answers with positive exponents.\r\n<ol>\r\n \t<li>[latex]{\\left(\\dfrac{4}{{z}^{11}}\\right)}^{3}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(\\dfrac{-1}{{t}^{2}}\\right)}^{27}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(\\dfrac{4xy^2}{x^3 {y}^{-2}}\\right)}^{-2}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"660878\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"660878\"]\r\n<ol>\r\n \t<li>[latex]{\\left(\\dfrac{4}{{z}^{11}}\\right)}^{3}=\\dfrac{{\\left(4\\right)}^{3}}{{\\left({z}^{11}\\right)}^{3}}=\\dfrac{64}{{z}^{11\\cdot 3}}=\\dfrac{64}{{z}^{33}}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(\\dfrac{-1}{{t}^{2}}\\right)}^{27}=\\dfrac{{\\left(-1\\right)}^{27}}{{\\left({t}^{2}\\right)}^{27}}=\\dfrac{-1}{{t}^{2\\cdot 27}}=\\dfrac{-1}{{t}^{54}}=-\\dfrac{1}{{t}^{54}}[\/latex]<\/li>\r\n \t<li>[latex]{\\left(\\dfrac{4xy^2}{x^3 {y}^{-2}}\\right)}^{-2} = {\\left(\\dfrac{x^3\\cdot {y}^{-2}}{4\\cdot x\\cdot y^2}\\right)}^2=\\dfrac{x^6\\cdot {y}^{-4}}{4^2\\cdot x^2\\cdot y^4}=\\dfrac{x^6}{16\\cdot x^2\\cdot y^4\\cdot y^4}=\\dfrac{{x}^{^{6-2}}}{16\\cdot {y}^{^{4+4}}}=\\dfrac{x^4}{16y^8}[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<span style=\"color: #000000;\">The following video provides more examples of simplifying expressions using the power of a quotient and other exponent rules.<\/span>\r\n\r\nhttps:\/\/youtu.be\/BoBe31pRxFM\r\n\r\nThe video below works through some examples of simplifying expressions that contain powers and negative exponents.\r\n\r\nhttps:\/\/youtu.be\/OYx7A0h2DII?si=bqfa5HUp_tvqv95O\r\n\r\n&nbsp;\r\n<h2 id=\"pf\" style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Polynomial Functions and Expressions<\/span><\/h2>\r\nYou may see a resemblance between expressions and polynomials which we have been studying in this course. \u00a0Polynomials are a special sub-group of mathematical expressions and equations. A polynomial is an expression consisting of the sum or difference of terms in which each term is a\u00a0real\u00a0number, a variable, or the product of a\u00a0real\u00a0number and variable(s) with non-negative integer exponent(s). Non negative integers are\u00a0[latex]0, 1, 2, 3, 4[\/latex], ...\r\nThe basic building block of a polynomial is a <b>monomial<\/b>. A monomial is one term and can be a number, a variable, or the product of a number and variable(s) with an exponent. The number part of the term is called the <b>coefficient<\/b>.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01183539\/image003.jpg\" alt=\"The expression 6x to the power of 3. 6 is the coefficient, x is the variable, and the power of 3 is the exponent.\" width=\"183\" height=\"82\" \/>\r\n\r\nA polynomial containing two terms, such as [latex]2x - 9[\/latex], is called a <strong>binomial<\/strong>. A polynomial containing three terms, such as [latex]-3{x}^{2}+8x - 7[\/latex], is called a <strong>trinomial<\/strong>. We can find the <strong>degree<\/strong> of a single variable polynomial by identifying the highest power of the variable that occurs in the polynomial. You will discuss the degree of multivariable polynomials in later courses. The term with the highest degree is called the <strong>leading term<\/strong> because it is usually written first. The coefficient of the leading term is called the <strong>leading coefficient<\/strong>. When a polynomial is written so that the powers on a specified variable are descending, meaning the power of the term decreases for each succeeding term, we say that it is in standard form. It is important to note that polynomials only have integer exponents.<img class=\"wp-image-2550 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/15150341\/Screen-Shot-2016-07-15-at-8.03.13-AM-300x150.png\" alt=\"4x^3 - 9x^2 + 6x, with the text &quot;degree = 3&quot; and an arrow pointing at the exponent on x^3, and the text &quot;leading term =4&quot; with an arrow pointing at the 4. \" width=\"504\" height=\"252\" \/>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFor the following polynomials, identify the degree, the leading term, and the leading coefficient.\r\n<ol>\r\n \t<li>[latex]3+2{x}^{2}-4{x}^{3}[\/latex]<\/li>\r\n \t<li>[latex]5{t}^{5}-2{t}^{3}+7t[\/latex]<\/li>\r\n \t<li>[latex]6p-{p}^{3}-2[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"753071\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"753071\"]\r\n<ol>\r\n \t<li>The highest power of [latex]x[\/latex] is\u00a0[latex]3[\/latex], so the degree is\u00a0[latex]3[\/latex].\r\n<ul>\r\n \t<li>The leading term is the term containing that degree, [latex]-4{x}^{3}[\/latex].<\/li>\r\n \t<li>The leading coefficient is the coefficient of that term, [latex]-4[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The highest power of [latex]t[\/latex] is [latex]5[\/latex], so the degree is [latex]5[\/latex].\r\n<ul>\r\n \t<li>The leading term is the term containing that degree, [latex]5{t}^{5}[\/latex].<\/li>\r\n \t<li>The leading coefficient is the coefficient of that term, [latex]5[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>The highest power of [latex]p[\/latex] is [latex]3[\/latex], so the degree is [latex]3[\/latex].\r\n<ul>\r\n \t<li>The leading term is the term containing that degree, [latex]-{p}^{3}[\/latex].<\/li>\r\n \t<li>The leading coefficient is the coefficient of that term, [latex]-1[\/latex].<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nIn the following video, we will identify the terms, leading coefficient, and degree of a polynomial.\r\n\r\nhttps:\/\/youtu.be\/3u16B2PN9zk\r\n<h2>Add and Subtract Polynomials<\/h2>\r\nRecall from previous courses that we can add and subtract polynomials by combining like terms which are terms that contain the same variables raised to the same exponents. For example, [latex]5{x}^{2}[\/latex] and [latex]-2{x}^{2}[\/latex] are like terms and can be added to get [latex]3{x}^{2}[\/latex], but [latex]3x[\/latex] and [latex]3{x}^{2}[\/latex] are not like terms; therefore, they cannot be added.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum.\r\n<p style=\"text-align: center;\">[latex]\\left(12{x}^{2}+9x - 21\\right)+\\left(4{x}^{3}+8{x}^{2}-5x+20\\right)[\/latex]<\/p>\r\n<p style=\"text-align: left;\">[reveal-answer q=\"222892\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"222892\"]<\/p>\r\nYou can write one polynomial below the other, making sure to line up the like terms. Notice that the first polynomial does not have a [latex]x^3[\/latex] term.\r\n\r\n&nbsp;\r\n\r\n[latex]0{x}^{3}+12{x}^{2}+9x - 21\\\\ 4{x}^{3}+8{x}^{2}\\hspace{2mm}-5x+20[\/latex]\r\n\r\n&nbsp;\r\n<p style=\"text-align: left;\">Combine like terms, paying close attention to the signs.<\/p>\r\n&nbsp;\r\n\r\n[latex]\\hspace{15mm}12{x}^{2}+9x - 21\\\\ \\underline{+4{x}^{3}+8{x}^{2}-5x+20}\\\\ \\hspace{3mm}4{x}^{3}+20{x}^{2}+4x-1[\/latex]\r\n<p style=\"text-align: left;\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\nWhen you subtract polynomials, you will still be looking for like terms to combine, but you will need to pay attention to the sign of the terms you are combining. In the following example, we will show how to distribute the negative sign to each term of a polynomial that is being subtracted from another.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the difference.\r\n<p style=\"text-align: center;\">[latex]\\left(7{x}^{4}-{x}^{2}+6x+1\\right)-\\left(5{x}^{3}-2{x}^{2}+3x+2\\right)[\/latex]<\/p>\r\n<p style=\"text-align: left;\">[reveal-answer q=\"279648\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"279648\"]<\/p>\r\nSince we are subtracting all of the second polynomial from the first polynomial, start by distributing the negative through the parentheses of the second polynomial. This will change the sign of each term to its opposite and you will have:\r\n\r\n&nbsp;\r\n\r\n[latex]\\left(7{x}^{4}-{x}^{2}+6x+1\\right)-5{x}^{3}+2{x}^{2}-3x-2[\/latex]\r\n\r\n&nbsp;\r\n\r\nWrite the polynomials so that the like terms are lined up. Notice that the [latex]{x}^{3}[\/latex] term is missing from the first polynomial and the [latex]{x}^{4}[\/latex] term is missing from the second polynomial. Then combine the like terms together.\r\n\r\n&nbsp;\r\n\r\n[latex]\\hspace{5mm} 7{x}^{4}+0{x}^{3}-\\hspace{2mm}{x}^{2}+6x+1\\\\ \\underline{+0{x}^{4}-5{x}^{3}+2{x}^{2}-3x-2}\\\\ \\hspace{3mm}7{x}^{4}-5{x}^{3}+\\hspace{3mm}{x}^{2}+3x-1[\/latex]\r\n\r\n&nbsp;\r\n\r\n*Note that finding the difference between two polynomials is the same as adding the opposite of the second polynomial to the first.\r\n<p style=\"text-align: left;\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\nIn the following video, we show more examples of adding and subtracting polynomials.\r\n\r\nhttps:\/\/youtu.be\/jiq3toC7wGM\r\n<h2>Multiplying Polynomials<\/h2>\r\n<span style=\"background-color: #ffffff;\">Multiplying polynomials is a bit more challenging than adding and subtracting polynomials. We must use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. We then combine like terms.<\/span>\r\n\r\nThe following video will provide you with examples of using the distributive property to find the product of\u00a0monomials and polynomials.\r\n\r\nhttps:\/\/youtu.be\/bwTmApTV_8o\r\n<h2>Multiplying Two Binomials<\/h2>\r\nYou can use the distributive property when multiplying two binomials. In other words, multiply each term in the first binomial by each term in the second.\r\n<div class=\"textbox exercises\">\r\n<h3>EXAMPLE<\/h3>\r\nSimplify. [latex](x+4)(x-2)[\/latex]\r\n[reveal-answer q=\"101118\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"101118\"]\r\n\r\nDistribute the [latex]x[\/latex] over [latex](x-2)[\/latex], then distribute the [latex]4[\/latex] over [latex](x-2)[\/latex].\r\n\r\n[latex]\r\n\\begin{align}\r\n\\require{color}\r\n&amp;= x(x-2)+4(x-2)\\\\\r\n&amp;= {x}^{2}-2x+4x-8 &amp;&amp;\\color{blue}{\\textsf{multiply}}\\\\\r\n&amp;= {x}^{2}+2x-8 &amp;&amp;\\color{blue}{\\textsf{combine like terms}}\\\\\r\n\\end{align}\r\n[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h2>Using FOIL to Multiply Binomials<\/h2>\r\nThe acronym FOIL (First, Outer, Inner, Last) is a memory device to multiply two binomials. It is called the FOIL method because we multiply the\r\n<p style=\"text-align: center;\"><strong>F<\/strong>irst terms,\u00a0<strong>O<\/strong>uter terms,\u00a0<strong>I<\/strong>nner terms, and\u00a0<strong>L<\/strong>ast terms.<\/p>\r\n<img class=\"aligncenter\" src=\"data:image\/png;base64,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\" width=\"611\" height=\"516\" \/>\r\n\r\nThe FOIL method arises out of the distributive property. We are simply multiplying each term of the first binomial by each term of the second binomial and then combining like terms. <strong>FOIL method only works when multiplying a binomial by another binomial.<\/strong>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nUse FOIL to find the product. [latex](2x-18)(3x+3)[\/latex]\r\n[reveal-answer q=\"787670\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"787670\"]\r\n\r\nFind the product of the first terms.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200225\/CNX_CAT_Figure_01_04_004.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting 2 x and 3 x. On right is equation: 2 x times 3 x = 6 x squared.\" width=\"487\" height=\"52\" \/>\r\n\r\nFind the product of the outer terms.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200227\/CNX_CAT_Figure_01_04_005.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting 2 x in first expression and plus 3 in second expression. On right is equation:  2 x times 3 = 6 x. \" width=\"487\" height=\"52\" \/>\r\n\r\nFind the product of the inner terms.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200228\/CNX_CAT_Figure_01_04_006.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting negative 18 and 3 x. On right is equation: negative 18 times 3 x = negative 54 x.\" width=\"487\" height=\"52\" \/>\r\n\r\nFind the product of the last terms.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200229\/CNX_CAT_Figure_01_04_007.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting negative 18 and plus 3. On right is equation: negative 18 times 3 = negative 54. \" width=\"487\" height=\"52\" \/>\r\n[latex]\r\n\\begin{align}\r\n\\require{color}\r\n&amp;= 6{x}^{2}+6x - 54x - 54 \\\\ &amp;= 6{x}^{2}-48x - 54 &amp;&amp;\\color{blue}{\\text{combine like terms}}\\end{align}[\/latex]\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we show an example of how to use the FOIL method to multiply two binomials. Remember that the FOIL method is only used when multiplying two binomials.\r\n\r\nhttps:\/\/youtu.be\/_MrdEFnXNGA\r\n<h2>Using the Box Method to Multiply Polynomials<\/h2>\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Another method you can use to multiply binomials is the Box Method, where you can use a table to organize the terms as shown below. Let's use the Box Method to multiply [latex](4x-5)[\/latex] and [latex](2x+7)[\/latex]. Write one polynomial factor across the top and the other down the side. For each box in the table, multiply the term for that row by the term for that column. Then combine like terms to simplify. Notice that we need to keep the sign on each term when we write it in the table.<\/span><\/h3>\r\n&nbsp;\r\n<table style=\"width: 30%; border: 1px solid black;\" summary=\"A table with 3 rows and 3 columns. The first entry of the first row is empty, the second entry reads: four times x The third entry reads: negative 5. The first entry of the second row is labeled: two times x. The second entry reads:eight x squared. The third entry reads: negative ten times x. The first entry of the third row reads: positive seven. The second entry reads: twenty eight times x. The third entry reads: negative thirty five.\">\r\n<thead>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\"><\/td>\r\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]4x[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-5[\/latex]<\/td>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 19px;\">\r\n<td style=\"width: 138.4375px; height: 19px; border: 1px solid #999999;\">[latex]2x[\/latex]<\/td>\r\n<td style=\"width: 174.53125px; height: 19px; border: 1px solid #999999;\">[latex]8{x}^{2}[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 19px; border: 1px solid #999999;\">[latex]-10x[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\">[latex]+7[\/latex]<\/td>\r\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]28x[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-35[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n<p style=\"text-align: center;\">[latex]\r\n\\begin{align}\r\n\\require{color}\r\n(4x-5)(2x+7) &amp;= 8{x}^{2}-10x +28x - 35 \\\\ &amp;= 8{x}^{2}+18x - 35 &amp;&amp;\\color{blue}{\\text{combine like terms}}\\end{align}[\/latex]<\/p>\r\n\r\n<h2>Multiplying a Binomial with a Trinomial<\/h2>\r\nAnother type of polynomial multiplication problem is the product of a binomial and trinomial. Although the FOIL method cannot be used since there are more than two terms in a trinomial, you still use the distributive property to organize the individual products. Using the distributive property, each term in the binomial must be multiplied by each of the terms in the trinomial. For this example, we will show you two ways to organize all of the terms that result from multiplying polynomials with more than two terms. The most important part of the process is finding a way to organize terms.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the product using the Distributive Property. \u00a0[latex]\\left(3x-6\\right)\\left(5x^{2}+3x+10\\right)[\/latex]\r\n[reveal-answer q=\"637359\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"637359\"]\r\n<p style=\"text-align: left;\">Distribute the trinomial to each term in the binomial.\r\n[latex]\r\n\\begin{align}\r\n\\require{color}\r\n&amp;= 3x\\left(5x^{2}+3x+10\\right)-6\\left(5x^{2}+3x+10\\right)&amp;&amp;\\color{blue}{\\textsf{use the distributive property}}\\\\\r\n&amp;= 3x\\left(5x^{2}\\right)+3x\\left(3x\\right)+3x\\left(10\\right)-6\\left(5x^{2}\\right)-6\\left(3x\\right)-6\\left(10\\right) &amp;&amp; \\color{blue}{\\textsf{multiply}}\\\\\r\n&amp;= 15x^{3}+9x^{2}+30x-30x^{2}-18x-60\\\\\r\n&amp;= 15x^{3}+\\left(9x^{2}-30x^{2}\\right)+\\left(30x-18x\\right)-60 &amp;&amp; \\color{blue}{\\textsf{group like terms}}\\\\\r\n&amp;=15x^{3}-21x^{2}+12x-60 &amp;&amp; \\color{blue}{\\textsf{combine like terms}}\\\\ \\end{align}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nWe will now rework this example using the Box Method. The Box Method is good to use when you are multiplying a binomial by a trinomial because it can help you keep track of all of the terms involved.\r\n<div class=\"textbox exercises\">\r\n<h3>ExAMPLE<\/h3>\r\nFind the product using the Box Method. [latex](3x-6)(5{x}^{2}+3x+10)[\/latex]\r\n\r\n[reveal-answer q=\"530295\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"530295\"]\r\n<table style=\"width: 30%; border: 1px solid black;\" summary=\"A table with 3 rows and 4 columns. The first entry of the first row is empty, the second entry reads: five times x squared, the third entry reads: three times x, the fourth entry reads: positive ten. The first entry of the second row is labeled: three times x. The second entry reads: fifteen x cubed. The third entry reads: nine x squared. The fourth entry reads: thirty times x. The first entry of the third row reads: negative six. The second entry reads: negative thirty x squared. The third entry reads: negative eighteen times x. The fourth entry reads: negative sixty. The first entry of the fourth row is labeled: negative six. The second entry reads: negative thirty x squared. The third entry reads: negative eighteen times x. The fourth entry reads: negative sixty.\">\r\n<thead>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\"><\/td>\r\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]5x^2[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]+3x[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]+10[\/latex]<\/td>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 19px;\">\r\n<td style=\"width: 138.4375px; height: 19px; border: 1px solid #999999;\">[latex]3x[\/latex]<\/td>\r\n<td style=\"width: 174.53125px; height: 19px; border: 1px solid #999999;\">[latex]15{x}^{3}[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 19px; border: 1px solid #999999;\">[latex]9x^2[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]30x[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\">[latex]-6[\/latex]<\/td>\r\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]-30x^2[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-18x[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-60[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLet's line up the like terms on top of each other so that it is easier to combine the like terms together.\r\n\r\n[latex]\r\n15x^{3}+9x^{2}+30x\\\\\r\n\\underline{\\hspace{1cm}-30x^{2}-18x-60}\\\\\r\n15x^{3}-21x^{2}+12x-60[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Let's look at another example where we are multiplying a binomial with a trinomial. Pay attention to the signs on the terms. Forgetting a negative sign is the easiest mistake to make in this case.<\/span><\/h3>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the product using the Distributive Property.\r\n\r\n[latex]\\left(2x+1\\right)\\left(3{x}^{2}-x+4\\right)[\/latex]\r\n\r\n[reveal-answer q=\"485882\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"485882\"]\r\n[latex]\\begin{align}\\require{color}\r\n&amp;= 2x\\left(3{x}^{2}-x+4\\right)+1\\left(3{x}^{2}-x+4\\right) &amp;&amp; \\color{blue}{\\textsf{use the distributive property}}\\\\\r\n&amp;= \\left(6{x}^{3}-2{x}^{2}+8x\\right)+\\left(3{x}^{2}-x+4\\right) &amp;&amp; \\color{blue}{\\textsf{multiply}}\\\\\r\n&amp;= 6{x}^{3}+\\left(-2{x}^{2}+3{x}^{2}\\right)+\\left(8x-x\\right)+4 &amp;&amp; \\color{blue}{\\textsf{group like terms}}\\\\\r\n&amp;= 6{x}^{3}+{x}^{2}+7x+4 &amp;&amp; \\color{blue}{\\textsf{combine like terms}}\\end{align}[\/latex]\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nWe will rework the above example using the Box Method\r\n<div class=\"textbox exercises\">\r\n<h3>ExAMPLE<\/h3>\r\nFind the product using the Box Method.\r\n\r\n[latex]\\left(2x+1\\right)\\left(3{x}^{2}-x+4\\right)[\/latex]\r\n\r\n[reveal-answer q=\"320112\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"320112\"]\r\n<table style=\"width: 30%;\" summary=\"A table with 3 rows and 4 columns. The first entry of the first row is empty, the others are labeled: three times x squared, negative x, and positive four. The first entry of the second row is labeled: two times x. The second entry reads: six times x cubed. The third entry reads: negative two times x squared. The fourth entry reads: eight times x. The first entry of the third row reads: positive one. The second entry reads: three times x squared. The third entry reads: negative x. The fourth entry reads: four.\">\r\n<thead>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\"><\/td>\r\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]3x^2[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-x[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]+4[\/latex]<\/td>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr style=\"height: 19px;\">\r\n<td style=\"width: 138.4375px; height: 19px; border: 1px solid #999999;\">[latex]2x[\/latex]<\/td>\r\n<td style=\"width: 174.53125px; height: 19px; border: 1px solid #999999;\">[latex]6{x}^{3}[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 19px; border: 1px solid #999999;\">[latex]-2x^2[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]8x[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 14px;\">\r\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\">[latex]+1[\/latex]<\/td>\r\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]3x^2[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-x[\/latex]<\/td>\r\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]4[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nLet's line up the like terms on top of each other so that it is easier to combine the like terms together.\r\n\r\n[latex]\r\n6x^{3}-2x^{2}+8x\\\\\r\n\\underline{\\hspace{13mm}3x^{2}\\hspace{2mm}-x+4}\\\\\r\n6x^{3}\\hspace{2mm}+x^{2}+7x+4[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we show more examples of multiplying polynomials.\r\n\r\nhttps:\/\/youtu.be\/bBKbldmlbqI\r\n\r\n&nbsp;","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Simplify expressions by applying the Properties of Exponents<\/li>\n<li>Multiply polynomials<\/li>\n<\/ul>\n<\/div>\n<p>A common language is needed in order to communicate mathematical ideas clearly and efficiently. <strong>Exponential notation<\/strong>\u00a0was developed to write repeated multiplication more efficiently. For example, growth occurs in living organisms by the division of cells. One type of cell divides\u00a0[latex]2[\/latex] times in an hour. So in\u00a0[latex]12[\/latex] hours, the cell will divide [latex]\\overbrace{2\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}\\cdot{2}}^{2^{12}}[\/latex] times.\u00a0This can be expressed\u00a0more efficiently as [latex]2^{12}[\/latex]. In this section we will learn how to simplify and perform mathematical operations such as multiplication and division on terms that have exponents.<\/p>\n<h2>Exponential Expressions<\/h2>\n<p>We use exponential notation to write repeated multiplication. For example, [latex]10\\cdot10\\cdot10[\/latex] can be written more succinctly as [latex]10^{3}[\/latex]. The\u00a0[latex]10[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>base<\/b>. The\u00a0[latex]3[\/latex] in [latex]10^{3}[\/latex]<sup>\u00a0<\/sup>is called the <b>exponent<\/b>. The expression [latex]10^{3}[\/latex] is called the exponential expression. Knowing the names for the parts of an exponential expression will help you learn how to perform mathematical operations on them.<\/p>\n<p style=\"text-align: center;\">[latex]\\text{base}\\rightarrow10^{3\\leftarrow\\text{exponent}}[\/latex]<\/p>\n<p>[latex]10^{3}[\/latex] is read as \u201c[latex]10[\/latex] to the third power\u201d or \u201c[latex]10[\/latex] cubed.\u201d It means [latex]10\\cdot10\\cdot10[\/latex], or [latex]1,000[\/latex].<\/p>\n<p>[latex]8^{2}[\/latex]\u00a0is read as \u201c[latex]8[\/latex] to the second power\u201d or \u201c[latex]8[\/latex] squared.\u201d It means [latex]8\\cdot8[\/latex], or [latex]64[\/latex].<\/p>\n<p>[latex]5^{4}[\/latex]\u00a0is read as \u201c[latex]5[\/latex] to the fourth power.\u201d It means [latex]5\\cdot5\\cdot5\\cdot5[\/latex], or\u00a0[latex]625[\/latex].<\/p>\n<p>[latex]b^{5}[\/latex]\u00a0is read as \u201c[latex]b[\/latex] to the fifth power.\u201d It means [latex]{b}\\cdot{b}\\cdot{b}\\cdot{b}\\cdot{b}[\/latex]. Its value will depend on the value of [latex]b[\/latex].<\/p>\n<p>The exponent applies only to the number or the variable that it is attached to. Therefore, in the expression [latex]xy^{4}[\/latex],\u00a0only the [latex]y[\/latex] is affected by the\u00a0[latex]4[\/latex]. [latex]xy^{4}[\/latex]\u00a0means [latex]{x}\\cdot{y}\\cdot{y}\\cdot{y}\\cdot{y}[\/latex]. The [latex]x[\/latex] is <strong>not<\/strong> being raised to the 4th power.<\/p>\n<p>Consider an expression like [latex]\u22123^{4}[\/latex]. In the previous paragraph, <strong>only<\/strong> the [latex]3[\/latex] is being raised to the 4th power (not the negative). You can rewrite the expression as [latex]-1\\cdot3^{4}[\/latex] which means [latex]\u20131\\cdot\\left(3\\cdot3\\cdot3\\cdot3\\right)[\/latex], or [latex]\u221281[\/latex].<\/p>\n<p>If [latex]\u22123[\/latex] is to be the base, it must be written using parentheses as [latex]\\left(\u22123\\right)^{4}[\/latex], which means [latex](\u22123)\\cdot(\u22123)\\cdot(\u22123)\\cdot(\u22123)[\/latex], or\u00a0[latex]81[\/latex].<\/p>\n<p>Likewise,\u00a0[latex]\\left(\u2212x\\right)^{4}=\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)\\cdot\\left(\u2212x\\right)=x^{4}[\/latex], while [latex]\u2212x^{4}=\\ \u20131\\cdot\\left(x\\cdot x\\cdot x\\cdot x\\right)[\/latex].<\/p>\n<p class=\"no-indent\">In the following video, you are provided more examples of applying exponents to various bases.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Simplify  Basic Exponential Expressions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ocedY91LHKU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox shaded\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-2132\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01182614\/traffic-sign-160659-300x265.png\" alt=\"Caution Sign\" width=\"75\" height=\"66\" \/>Caution! Whether to include a negative sign as part of a base or not often leads to confusion. To clarify\u00a0whether a negative sign is applied before or after the exponent, here is an example.<\/p>\n<p>What is the difference in the way you would evaluate these two terms?<\/p>\n<ol>\n<li style=\"text-align: left;\">[latex]-{3}^{2}[\/latex]<\/li>\n<li style=\"text-align: left;\">[latex]{\\left(-3\\right)}^{2}[\/latex]<\/li>\n<\/ol>\n<p>To evaluate 1), you would apply the exponent to the three first, then apply the negative sign last, like this:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{align}&\\quad\\,-3^2\\\\ &=-\\left({3}^{2}\\right)&\\\\ &=-\\left(9\\right) &\\\\ &= -9\\end{align}[\/latex]<\/p>\n<p style=\"text-align: left;\">To evaluate 2), you would apply the exponent to the negative [latex]3[\/latex]:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{align}&\\quad\\;\\left(-3\\right)^{2}&\\\\ &=\\left(-3\\right)\\cdot\\left(-3\\right)&\\\\ &={ 9}\\end{align}[\/latex]<\/p>\n<p style=\"text-align: left;\">The key to remembering this is to follow the order of operations. The first expression does not include parentheses so you would apply the exponent to the integer [latex]3[\/latex] first, then apply the negative sign. The second expression includes parentheses, so hopefully you will remember that the negative sign also gets squared.<\/p>\n<\/div>\n<h2><\/h2>\n<h2>Properties of Exponents<\/h2>\n<p>Here is an overview of the properties of exponents. For a more detailed explanation and examples of these properties, please click on the property in the table you would like to review to or scroll down to corresponding section below.<\/p>\n<p>If you do not need to review the properties of exponents, you can skip down the page to <a class=\"anchorLink\" href=\"#pf\">Polynomial Functions and Expressions<\/a> where you can review adding, subtracting, and multiplying polynomial expressions and also review evaluating polynomial functions.<\/p>\n<table style=\"width: 70%;\">\n<caption style=\"caption-side: top; font-size: large;\">Properties of Exponents<br \/>\n<em>Assume denominators do not equal zero and [latex]m[\/latex] and [latex]n[\/latex] represent integers<\/em><\/caption>\n<thead>\n<tr>\n<th>\u00a0Name<\/th>\n<th>Property<\/th>\n<th>Example<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><a class=\"anchorLink\" href=\"#product\">Product Rule<\/a><\/td>\n<td>[latex]{\\large a^{m}\\cdot{a}^{n}=a^{m+n}}[\/latex]<\/td>\n<td>[latex]{\\large x^{3}\\cdot{x}^{2}=x^{3+2}=x^5}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><a class=\"anchorLink\" href=\"#quotient\">Quotient Rule<\/a><\/td>\n<td>[latex]{\\large \\dfrac{a^{m}}{{a}^{n}}=a^{m-n}}[\/latex]<\/td>\n<td>[latex]{\\large \\dfrac{x^{7}}{{x}^{4}}=x^{7-4}=x^3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><a class=\"anchorLink\" href=\"#power\">Power Rule<\/a><\/td>\n<td>[latex]{\\large \\left(a^{m}\\right)^{n}=a^{m\\cdot{n}}}[\/latex]<\/td>\n<td>[latex]{\\large \\left(x^{2}\\right)^{4}=x^{2\\cdot{4}}=x^8}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><a class=\"anchorLink\" href=\"#p of p\">Power of a Product Rule<\/a><\/td>\n<td>[latex]{\\large \\left(ab\\right)^{n}=a^{n}\\cdot b^{n}}[\/latex]<\/td>\n<td>[latex]{\\large \\left(2y\\right)^{3}=2^{3}\\cdot y^{3}=8y^3}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><a class=\"anchorLink\" href=\"#p of q\">Power of a Quotient Rule<\/a><\/td>\n<td>[latex]{\\large \\left(\\dfrac{a}{b}\\right)^{n}=\\dfrac{{a}^{n}}{{b}^{n}}, b \\ne{0}}[\/latex]<\/td>\n<td>[latex]{\\large \\left(\\dfrac{x}{3}\\right)^{2}=\\dfrac{{x}^{2}}{{3}^{2}}=\\dfrac{x^2}{9}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><a class=\"anchorLink\" href=\"#zero\">Zero Exponent Rule<\/a><\/td>\n<td>[latex]{\\large \\left({a}\\right)^{0}=1,{a} \\ne{0}}[\/latex]<\/td>\n<td>[latex]{\\large \\left({-4x^5}\\right)^{0}=1}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><a class=\"anchorLink\" href=\"#negative\">Negative Exponent Rule<\/a><\/td>\n<td><span style=\"background-color: #ffffff;\">[latex]{\\large {a}^{-n}=\\dfrac{1}{{a}^{n}}, {a} \\ne{0}}[\/latex]<\/span><\/td>\n<td>[latex]{\\large {x}^{-4}=\\dfrac{1}{{x}^{4}}}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><\/h2>\n<h2 id=\"product\">Product Rule to Multiply Exponential Expressions<\/h2>\n<p>What happens if you multiply two numbers in exponential form with the same base? Consider the expression [latex]{2}^{3}{2}^{4}[\/latex]. Exponents are repeated multiplication so we can Expand each exponent as [latex]\\left(2\\cdot2\\cdot2\\right)\\left(2\\cdot2\\cdot2\\cdot2\\right)[\/latex] or [latex]2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2\\cdot2[\/latex]. In exponential form, you would write the product as [latex]2^{7}[\/latex]. Notice that [latex]7[\/latex] is the sum of the original two exponents,\u00a0[latex]3[\/latex] and\u00a0[latex]4[\/latex].<\/p>\n<p>What about [latex]{x}^{2}{x}^{6}[\/latex]? This can be written as [latex]\\left(x\\cdot{x}\\right)\\left(x\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\right)=x\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}\\cdot{x}[\/latex] or [latex]x^{8}[\/latex]. And, once again, [latex]8[\/latex] is the sum of the original two exponents. This concept can be generalized in the following way:<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>The Product Rule for Exponents<\/h3>\n<p>For any number [latex]a[\/latex] and any integers [latex]m[\/latex] and [latex]n[\/latex],<\/p>\n<p>[latex]\\left(a^{m}\\right)\\left(a^{n}\\right) = a^{m+n}[\/latex].<\/p>\n<p>If [latex]m[\/latex], [latex]n[\/latex], or [latex]m+n[\/latex] is [latex]0[\/latex] or negative, then [latex]a[\/latex] cannot be [latex]0[\/latex].<\/p>\n<p>To multiply exponential expressions with the same base, add the exponents.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Write each of the following products with a single base. Do not simplify further.<\/p>\n<ol>\n<li>[latex]{t}^{5}\\cdot {t}^{3}[\/latex]<\/li>\n<li>[latex]{-3x^2}\\cdot {4x^5}[\/latex]<\/li>\n<li>[latex]{x}^{2}\\cdot {x}^{5}\\cdot {x}^{3}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q772709\">Show Solution<\/span><\/p>\n<div id=\"q772709\" class=\"hidden-answer\" style=\"display: none\">\n<p>Use the product rule to simplify each expression.<\/p>\n<ol>\n<li>[latex]{t}^{5}\\cdot {t}^{3}={t}^{5+3}={t}^{8}[\/latex]<\/li>\n<li>[latex]{-3x^2}\\cdot {4x^5}={-3}\\cdot {4}\\cdot{x}^{2+5}=-12x^7[\/latex]<\/li>\n<li>[latex]{x}^{2}\\cdot {x}^{5}\\cdot {x}^{3}={x}^{2+5+3}={x}^{10}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<div style=\"text-align: center;\"><\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the following video, you will see more examples of using the product rule for exponents to simplify expressions.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-2\" title=\"Simplify Expressions Using the Product Rule of Exponents (Basic)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/P0UVIMy2nuI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"quotient\">Quotient Rule to Divide Exponential Expressions<\/h2>\n<p>Let us look at dividing terms containing exponential expressions. What happens if you divide two numbers in exponential form with the same base? Consider the following expression: [latex]\\dfrac{7^5}{7^2}[\/latex]. You can rewrite the expression as [latex]\\dfrac{7\\cdot 7\\cdot 7\\cdot 7\\cdot 7}{7\\cdot 7}[\/latex].<\/p>\n<p>Then you can divide out the common factors of 7 in the numerator and denominator:<\/p>\n<p>[latex]\\require{color}\\dfrac{\\color{red}\\cancel{\\color{black}7} \\color{black} \\cdot \\color{red}\\cancel{\\color{black}7} \\color{black} \\cdot 7 \\cdot 7 \\cdot 7}{\\color{red}\\cancel{\\color{black}7} \\color{black} \\cdot \\color{red}\\cancel{\\color{black}7 \\color{black}}}[\/latex]<\/p>\n<h2><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Finally, this expression can be rewritten as [latex]7^{3}[\/latex]\u00a0using exponential notation. Notice that the exponent,\u00a0[latex]3[\/latex], is the difference between the two exponents in the original expression,\u00a0[latex]5[\/latex] and\u00a0[latex]2[\/latex]. So,\u00a0[latex]\\dfrac{7^5}{7^2}=7^{5-2}=7^{3}[\/latex].<\/span><\/h2>\n<h2><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Be careful that you subtract the exponent in the denominator from the exponent in the numerator. So, to divide two exponential expressions with the same base, subtract the exponents.<\/span><\/h2>\n<div class=\"textbox key-takeaways\">\n<h3>The Quotient (Division) Rule for Exponents<\/h3>\n<p>For any non-zero number [latex]a[\/latex] and any integers [latex]m[\/latex] and [latex]n[\/latex]:<\/p>\n<p>[latex]\\displaystyle \\dfrac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}, a \\ne 0[\/latex]<\/p>\n<p>To divide exponential expressions with the same base, subtract the exponents.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3><span style=\"font-size: 1em;\">Example<\/span><\/h3>\n<p>Write each of the following products with a single base. Do not simplify further.<\/p>\n<ol>\n<li>[latex]\\dfrac{{\\left(-2\\right)}^{14}}{{\\left(-2\\right)}^{9}}[\/latex]<\/li>\n<li>[latex]\\dfrac{{t}^{23}}{{t}^{15}}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q978732\">Show Solution<\/span><\/p>\n<div id=\"q978732\" class=\"hidden-answer\" style=\"display: none\">\n<p>Use the quotient rule to simplify each expression.<\/p>\n<ol>\n<li>[latex]\\dfrac{{\\left(-2\\right)}^{14}}{{\\left(-2\\right)}^{9}}={\\left(-2\\right)}^{14 - 9}={\\left(-2\\right)}^{5}=(-2)\\cdot(-2)\\cdot(-2)\\cdot(-2)\\cdot(-2) = -32[\/latex]<\/li>\n<li>[latex]\\dfrac{{t}^{23}}{{t}^{15}}={t}^{23 - 15}={t}^{8}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\">In the following video, you will see more examples of using the quotient rule for exponents.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Simplify Expressions Using the Quotient Rule of Exponents (Basic)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/xy6WW7y_GcU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"power\">Raise Exponential Expressions to Powers<\/h2>\n<p>Another word for exponent is power. You have likely seen or heard an example such as [latex]3^5[\/latex] can be described as\u00a0[latex]3[\/latex] raised to the\u00a0[latex]5[\/latex]th power. In this section we will further expand our capabilities with exponents. We will learn what to do when an expression with a\u00a0power\u00a0is raised to another power and what to do when two numbers or variables are multiplied and both are raised to a power. We will also learn what to do when numbers or variables that are divided are raised to a power. We will begin by raising exponential expressions to powers.<\/p>\n<p>Let us simplify [latex]\\left(5^{2}\\right)^{4}[\/latex].<\/p>\n<p>In this case, [latex]\\left(5^{2}\\right)^{4}[\/latex] indicates that the quantity [latex]5^2[\/latex]<sup>\u00a0<\/sup>is raised to the fourth power , so you multiply [latex]5^{2}[\/latex]<sup>\u00a0<\/sup>four times: [latex]\\left(5^{2}\\right)^{4}=5^{2}\\cdot5^{2}\\cdot5^{2}\\cdot5^{2}=5^{8}[\/latex]<sup>\u00a0<\/sup>(using the Product Rule\u2014add the exponents).<\/p>\n<p>We saw above that the answer is [latex]5^{8}[\/latex]. Notice that the new exponent is the same as the product of the original exponents: [latex]2\\cdot4=8[\/latex]. So, [latex]\\left(5^{2}\\right)^{4}=5^{2\\cdot4}=5^{8}[\/latex]\u00a0(which equals [latex]390,625[\/latex] if you do the multiplication).<\/p>\n<p>Likewise, [latex]\\left(x^{4}\\right)^{3}=x^{4\\cdot3}=x^{12}[\/latex].<\/p>\n<p>This leads to the <b>Power Rule for Exponents<\/b>. To simplify a power of a power, you multiply the exponents, keeping the base the same. For example, [latex]\\left(2^{3}\\right)^{5}=2^{15}[\/latex].<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>The Power Rule for Exponents<\/h3>\n<p>For any real number [latex]a[\/latex] and integers [latex]m[\/latex] and [latex]n[\/latex]:<\/p>\n<p>[latex]\\left(a^{m}\\right)^{n}=a^{m\\cdot{n}}[\/latex].<\/p>\n<p>If [latex]m[\/latex] or [latex]n[\/latex] is [latex]0[\/latex] or negative, then [latex]a[\/latex] must not be [latex]0[\/latex].<\/p>\n<p>When raising an exponential expression to a power, keep the base the same and multiply the exponents.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p><em>Take a moment to contrast in your mind <strong>how the power rule for exponents is different from the product rule for exponents. <\/strong>With the power rule you are multiplying the exponents but with the product rule you are adding the exponents.<\/em><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Write each of the following products with a single base. Do not simplify further.<\/p>\n<ol>\n<li>[latex]{\\left({x}^{2}\\right)}^{7}[\/latex]<\/li>\n<li>[latex]{\\left({\\left(-3\\right)}^{5}\\right)}^{11}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q841688\">Show Solution<\/span><\/p>\n<div id=\"q841688\" class=\"hidden-answer\" style=\"display: none\">\n<p>Use the power rule to simplify each expression.<\/p>\n<ol>\n<li>[latex]{\\left({x}^{2}\\right)}^{7}={x}^{2\\cdot 7}={x}^{14}[\/latex]<\/li>\n<li>[latex]{\\left({\\left(-3\\right)}^{5}\\right)}^{11}={\\left(-3\\right)}^{5\\cdot 11}={\\left(-3\\right)}^{55}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the following video, you will see more examples of using the power rule to simplify expressions with exponents.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Simplify Expressions Using the Power Rule of Exponents (Basic)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/VjcKU5rA7F8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Be careful to distinguish between uses of the <strong>product rule<\/strong> and the <strong>power rule<\/strong>.<\/p>\n<ul>\n<li>Using the <strong>product rule:<\/strong>\u00a0When multiplying expressions with exponents with the same base, keep the base, add the exponents.<\/li>\n<li>Using the <strong>power rule:<\/strong>\u00a0When raising an expression with an exponent to a power, keep the base and multiply the exponents.<\/li>\n<\/ul>\n<h2 id=\"zero\">Zero Exponent Rule<\/h2>\n<p>Above when we used the quotient rule we had expressions for which [latex]m[\/latex] is larger than [latex]n[\/latex] so that the difference [latex]m-n[\/latex] would never be zero or negative.<\/p>\n<p>What would happen if [latex]m[\/latex] and [latex]n[\/latex] were equal? In this case, we would use the <em>zero exponent rule of exponents<\/em> to simplify the expression to\u00a0[latex]1[\/latex]. To see how this is done, let us begin with an<span style=\"background-color: #ffffff;\"> example<\/span>.<\/p>\n<p>[latex]\\require{color}\\dfrac{t^8}{t^8}=\\dfrac{\\color{red}\\cancel{\\color{black}{t^8}}}{\\color{red}\\cancel{\\color{black}{t^8}}}=1[\/latex]<\/p>\n<p>If we were to simplify the original expression using the quotient rule, we would have: [latex]\\dfrac{{t}^{8}}{{t}^{8}}={t}^{8 - 8}={t}^{0}[\/latex]<\/p>\n<p>For both methods of simplifying to be true, then [latex]{t}^{0}=1[\/latex]. This is true for any nonzero real number, or any variable representing a nonzero real number. The sole exception is the expression [latex]{0}^{0}[\/latex]. This appears later in more advanced courses, but for now, we will consider the value to be indeterminate.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>The Zero Exponent Rule for Exponents<\/h3>\n<p>For any nonzero real number [latex]a[\/latex], the zero exponent rule of exponents states that<\/p>\n<div style=\"text-align: center;\">[latex]\\large{{a}^{0}=1}[\/latex]<\/div>\n<p>Any number (except [latex]0[\/latex]) raised to the zero power is [latex]1[\/latex].<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify each expression using the zero exponent rule of exponents.<\/p>\n<ol>\n<li>[latex]-3^2\\cdot{(-5x^2)}^{0}[\/latex]<\/li>\n<li>[latex]\\dfrac{-3{x}^{5}}{{x}^{5}}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q375469\">Show Solution<\/span><\/p>\n<div id=\"q375469\" class=\"hidden-answer\" style=\"display: none\">\n<p>Use the zero exponent and other rules to simplify each expression.<\/p>\n<p>1.<\/p>\n<p>[latex]\\begin{align}-3^2\\cdot{(-5x^2)}^{0} &=-(3\\cdot 3)\\cdot 1 && \\color{blue}{\\textsf{simplify exponents}}\\\\ &= -(9)\\cdot1 && \\color{blue}{\\textsf{multiply}}\\\\ &=-9\\end{align}[\/latex]<\/p>\n<p>2.<\/p>\n<p>[latex]\\begin{align}\\dfrac{-3{x}^{5}}{{x}^{5}} &= -3\\cdot \\dfrac{{x}^{5}}{{x}^{5}}\\\\ &= -3\\cdot {x}^{5 - 5}\\\\ &= -3\\cdot {x}^{0} && \\color{blue}{\\textsf{subtract exponents}}\\\\ &= -3\\cdot 1 && \\color{blue}{\\textsf{multiply}}\\\\ &= -3 \\end{align}[\/latex]<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the following video, you will see more examples of simplifying expressions whose exponents may be zero.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Simplify Expressions Using the Quotient and Zero Exponent Rules\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/rpoUg32utlc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"negative\">Negative Exponent Rule<\/h2>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Can we simplify [latex]\\dfrac{{h}^{3}}{{h}^{5}}[\/latex]? <\/span><\/h3>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">When [latex]n\\ is\\ larger\\ than\\ m[\/latex], the difference [latex]m-n[\/latex] is negative. We can use the <\/span><em style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">negative rule of exponents<\/em><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\"> to simplify the expression so that it is easier to understand. <\/span><\/h3>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Let&#8217;s look at an example to clarify this idea. Given the expression:\u00a0<\/span><span style=\"color: #373d3f; font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2;\">[latex]\\dfrac{{h}^{3}}{{h}^{5}}[\/latex].\u00a0<\/span><\/h3>\n<p>Let&#8217;s expand the numerator and denominator and then divide out the common factors to simplify.<\/p>\n<p>[latex]\\begin{align}  \\dfrac{h^3}{h^5} &= \\dfrac{h\\cdot h\\cdot h}{h\\cdot h\\cdot h\\cdot h\\cdot h}\\\\  &= \\dfrac{{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}}  {{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}\\cdot{\\color{red}\\cancel{\\color{black}{h}}}\\cdot h\\cdot h}\\\\  &= \\dfrac{1}{h\\cdot h}\\\\  &= \\dfrac{1}{h^2}  \\end{align}[\/latex]<\/p>\n<p>Or, we can simplify using the Quotient Rule:<\/p>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">[latex]\\begin{array}{ccc}\\hfill \\dfrac{{h}^{3}}{{h}^{5}}& =& {h}^{3 - 5}\\hfill \\\\ & =& \\text{ }{h}^{-2}\\hfill \\end{array}[\/latex]<\/span><\/h3>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Putting the answers together, we have [latex]{h}^{-2}=\\dfrac{1}{{h}^{2}}[\/latex]. This is true for any nonzero real number, or any variable representing a nonzero real number.<\/span><\/h3>\n<div class=\"textbox key-takeaways\">\n<h3>The Negative Rule of Exponents<\/h3>\n<p>For any nonzero real number [latex]a[\/latex] and any integer [latex]n[\/latex], the negative rule of exponents states that<\/p>\n<div style=\"text-align: center;\">[latex]\\large{{a}^{-n}=\\dfrac{1}{{a}^{n}}} , a\\ne 0[\/latex]<\/div>\n<div><\/div>\n<p>When the exponent is negative, write the reciprocal of the base raised to the positive exponent.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify. Write answers with positive exponents.<\/p>\n<ol>\n<li>[latex]\\dfrac{y^3}{{y}^{-4}}[\/latex]<\/li>\n<li>[latex]{-3}^{-2}[\/latex]<\/li>\n<li>[latex]\\dfrac{{(2b) }^{3}}{{(2b) }^{7}}[\/latex]<\/li>\n<li>[latex]\\dfrac{{z}^{2}\\cdot z}{{z}^{4}}[\/latex]<\/li>\n<li>[latex]\\dfrac{{\\left(-5{t}^{3}\\right)}^{4}}{{\\left(-5{t}^{3}\\right)}^{7}}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q552758\">Show Solution<\/span><\/p>\n<div id=\"q552758\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]\\dfrac{y^3}{{y}^{-4}}=y^3 \\cdot y^4=y^7[\/latex]<\/li>\n<li>[latex]{-3}^{-2}= -1\\cdot {3}^{-2}=\\dfrac{-1}{3^2}=\\dfrac{-1}{3\\cdot 3}=\\dfrac{-1}{9}[\/latex]<\/li>\n<li>[latex]\\dfrac{{(2b) }^{3}}{{(2b)}^{7}}={(2b)}^{3 - 7}={(2b) }^{-4}=\\dfrac{1}{{(2b)}^{4}}=\\dfrac{1}{2^4 \\cdot {b}^{4}}=\\dfrac{1}{16b^4}[\/latex]<\/li>\n<li>[latex]\\dfrac{{z}^{2}\\cdot z}{{z}^{4}}=\\dfrac{{z}^{2+1}}{{z}^{4}}=\\dfrac{{z}^{3}}{{z}^{4}}={z}^{3 - 4}={z}^{-1}=\\dfrac{1}{z}[\/latex]<\/li>\n<li>[latex]\\dfrac{{\\left(-5{t}^{3}\\right)}^{4}}{{\\left(-5{t}^{3}\\right)}^{7}}={\\left(-5{t}^{3}\\right)}^{4 - 7}={\\left(-5{t}^{3}\\right)}^{-3}=\\dfrac{1}{{\\left(-5{t}^{3}\\right)}^{3}}=\\dfrac{1}{(-5)^3 \\cdot {(t^3)}^{3}}=\\dfrac{1}{-125 t^9}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #000000;\">In the following video, you will see examples of simplifying expressions with negative exponents.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Simplify Expressions Using the Quotient and Negative Exponent Rules\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Gssi4dBtAEI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Combine Exponent Rules to Simplify Expressions<\/h2>\n<p>Now we will combine the use of the product and quotient rules to simplify expressions whose terms may have negative or zero exponents.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Write each of the following products with a single base. Write answers with positive exponents.<\/p>\n<ol>\n<li>[latex]{b}^{2}\\cdot {b}^{-8}[\/latex]<\/li>\n<li>[latex]{\\left(-x\\right)}^{5}\\cdot {\\left(-x\\right)}^{-5}[\/latex]<\/li>\n<li>[latex]\\dfrac{-7z}{{\\left(-7z\\right)}^{3}}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q163692\">Show Solution<\/span><\/p>\n<div id=\"q163692\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]{b}^{2}\\cdot {b}^{-8}={b}^{2 - 8}={b}^{-6}=\\dfrac{1}{{b}^{6}}[\/latex]<\/li>\n<li>[latex]{\\left(-x\\right)}^{5}\\cdot {\\left(-x\\right)}^{-5}={\\left(-x\\right)}^{5 - 5}={\\left(-x\\right)}^{0}=1[\/latex]<\/li>\n<li>[latex]\\dfrac{-7z}{{\\left(-7z\\right)}^{3}}=\\dfrac{{\\left(-7z\\right)}^{1}}{{\\left(-7z\\right)}^{3}}={\\left(-7z\\right)}^{1 - 3}={\\left(-7z\\right)}^{-2}=\\dfrac{1}{{\\left(-7z\\right)}^{2}}=\\dfrac{1}{(-7)^2 \\cdot z^2}=\\dfrac{1}{49z^2}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>The following video shows more examples of how to combine the use of the product and quotient rules to simplify expressions whose terms may have negative or zero exponents.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-7\" title=\"Simplify Expressions Using Exponent Rules (Product, Quotient, Zero Exponent)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/EkvN5tcp4Cc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"p of p\">Finding the Power of a Product<\/h2>\n<p>To simplify the power of a product of two exponential expressions, we can use the <em>power of a product rule of exponents\u00a0<\/em>which breaks up the power of a product of factors into the product of the powers of the factors.<br \/>\nFor instance, consider [latex]{\\left(pq\\right)}^{3}[\/latex].<\/p>\n<p>We begin by using the associative and commutative properties of multiplication to regroup the factors.<\/p>\n<p>[latex]\\begin{array}{ccc}\\hfill {\\left(pq\\right)}^{3}& =& \\stackrel{3\\text{ factors}}{{\\left(pq\\right)\\cdot \\left(pq\\right)\\cdot \\left(pq\\right)}}\\hfill \\\\ & =& p\\cdot q\\cdot p\\cdot q\\cdot p\\cdot q\\hfill \\\\ & =& \\stackrel{3\\text{ factors}}{{p\\cdot p\\cdot p}}\\cdot \\stackrel{3\\text{ factors}}{{q\\cdot q\\cdot q}}\\hfill \\\\ & =& {p}^{3}\\cdot {q}^{3}\\hfill \\end{array}[\/latex]<\/p>\n<p>In other words, [latex]{\\left(pq\\right)}^{3}={p}^{3}\\cdot {q}^{3}[\/latex].<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>The Power of a Product Rule for Exponents<\/h3>\n<p>For any real numbers [latex]a[\/latex] and [latex]b[\/latex] and any integer [latex]n[\/latex], the power of a product rule of exponents states that<\/p>\n<div style=\"text-align: center;\">[latex]\\large{\\left(a \\cdot b\\right)}^{n}={a}^{n}\\cdot {b}^{n}[\/latex]<\/div>\n<div><\/div>\n<p>If [latex]n[\/latex] is [latex]0[\/latex] or negative, neither [latex]a[\/latex] nor [latex]b[\/latex] can be [latex]0[\/latex].<\/p>\n<p>When raising a product to a power, apply the exponent to each factor in the product. Then simplify the expression.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify each of the following products as much as possible using the power of a product rule. Write answers with positive exponents.<\/p>\n<ol>\n<li>[latex]{\\left(a{b}^{2}\\right)}^{3}[\/latex]<\/li>\n<li>[latex]{\\left(-2{w}^{3}\\right)}^{3}[\/latex]<\/li>\n<li>[latex]{\\left({j}^{3}{k}^{-2}\\right)}^{-4}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{{\\left(-2z\\right)}^{4}}[\/latex]<\/li>\n<li>[latex]{\\left({e}^{-2}{f}^{3}\\right)}^{7}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q788982\">Show Solution<\/span><\/p>\n<div id=\"q788982\" class=\"hidden-answer\" style=\"display: none\">\n<p>Use the product and quotient rules and the new definitions to simplify each expression.<\/p>\n<ol>\n<li>[latex]{\\left(a{b}^{2}\\right)}^{3}={\\left(a\\right)}^{3}\\cdot {\\left({b}^{2}\\right)}^{3}={a}^{1\\cdot 3}\\cdot {b}^{2\\cdot 3}={a}^{3}{b}^{6}[\/latex]<\/li>\n<li>[latex]{\\left(-2{w}^{3}\\right)}^{3}={\\left(-2\\right)}^{3}\\cdot {\\left({w}^{3}\\right)}^{3}=-8\\cdot {w}^{3\\cdot 3}=-8{w}^{9}[\/latex]<\/li>\n<li>[latex]{\\left({j}^{3}{k}^{-2}\\right)}^{-4}=({j^3})^{-4} \\cdot ({{k}^{-2}})^{-4}={j}^{-12} \\cdot k^8=\\dfrac{k^8}{{j}^{12}}[\/latex]<\/li>\n<li>[latex]\\dfrac{1}{{\\left(-2z\\right)}^{4}}=\\dfrac{1}{{\\left(-2\\right)}^{4}\\cdot {\\left(z\\right)}^{4}}=\\dfrac{1}{16{z}^{4}}[\/latex]<\/li>\n<li>[latex]{\\left({e}^{-2}{f}^{3}\\right)}^{7}={\\left({e}^{-2}\\right)}^{7}\\cdot {\\left({f}^{3}\\right)}^{7}={e}^{-2\\cdot 7}\\cdot {f}^{3\\cdot 7}={e}^{-14}{f}^{21}=\\dfrac{{f}^{21}}{{e}^{14}}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h3 style=\"text-align: center;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft wp-image-2132\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01183308\/traffic-sign-160659.png\" alt=\"Caution Sign.\" width=\"96\" height=\"83\" \/><\/h3>\n<div class=\"textbox shaded\">\n<p>Caution! Do not try to apply this rule to sums.<\/p>\n<p>Think about the expression\u00a0[latex]\\left(2+3\\right)^{2}[\/latex]<\/p>\n<p style=\"text-align: center;\">Does [latex]\\left(2+3\\right)^{2}[\/latex] equal [latex]2^{2}+3^{2}[\/latex]?<\/p>\n<p>No, it does not because of the order of operations!<\/p>\n<p style=\"text-align: center;\">[latex]\\left(2+3\\right)^{2}=5^{2}=25[\/latex]<\/p>\n<p style=\"text-align: center;\">and<\/p>\n<p style=\"text-align: center;\">[latex]2^{2}+3^{2}=4+9=13[\/latex]<\/p>\n<p>Therefore, you can only use this rule when the numbers inside the parentheses are being multiplied or divided.<\/p>\n<\/div>\n<p><span style=\"color: #000000; font-size: 1rem; text-align: initial;\">In the following video, \u00a0we provide more examples of how to find the power of a product.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-8\" title=\"Simplify Expressions Using Exponent Rules (Power of a Product)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/p-2UkpJQWpo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2 id=\"p of q\">Finding the Power of a Quotient<\/h2>\n<p>To simplify the power of a quotient of two expressions, we can use the <em>power of a quotient rule\u00a0<\/em>which states that the power of a quotient of factors is the quotient of the powers of the factors.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>The Power of a Quotient Rule of Exponents<\/h3>\n<p>For any real numbers [latex]a[\/latex] and [latex]b[\/latex] and any integer [latex]n[\/latex], the power of a quotient rule of exponents states that<\/p>\n<div style=\"text-align: center;\">[latex]\\large{\\left(\\frac{a}{b}\\right)}^{n}=\\frac{{a}^{n}}{{b}^{n}}, b \\ne 0[\/latex]<\/div>\n<div><\/div>\n<p>If [latex]n[\/latex] is negative or [latex]0[\/latex], then [latex]a[\/latex] cannot be [latex]0[\/latex].<\/p>\n<p>When raising a quotient to a power, apply the exponent to the numerator and denominator. Then simplify the expression.<\/p>\n<\/div>\n<div><\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify each of the following quotients as much as possible using the power of a quotient rule. Write answers with positive exponents.<\/p>\n<ol>\n<li>[latex]{\\left(\\dfrac{4}{{z}^{11}}\\right)}^{3}[\/latex]<\/li>\n<li>[latex]{\\left(\\dfrac{-1}{{t}^{2}}\\right)}^{27}[\/latex]<\/li>\n<li>[latex]{\\left(\\dfrac{4xy^2}{x^3 {y}^{-2}}\\right)}^{-2}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q660878\">Show Solution<\/span><\/p>\n<div id=\"q660878\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]{\\left(\\dfrac{4}{{z}^{11}}\\right)}^{3}=\\dfrac{{\\left(4\\right)}^{3}}{{\\left({z}^{11}\\right)}^{3}}=\\dfrac{64}{{z}^{11\\cdot 3}}=\\dfrac{64}{{z}^{33}}[\/latex]<\/li>\n<li>[latex]{\\left(\\dfrac{-1}{{t}^{2}}\\right)}^{27}=\\dfrac{{\\left(-1\\right)}^{27}}{{\\left({t}^{2}\\right)}^{27}}=\\dfrac{-1}{{t}^{2\\cdot 27}}=\\dfrac{-1}{{t}^{54}}=-\\dfrac{1}{{t}^{54}}[\/latex]<\/li>\n<li>[latex]{\\left(\\dfrac{4xy^2}{x^3 {y}^{-2}}\\right)}^{-2} = {\\left(\\dfrac{x^3\\cdot {y}^{-2}}{4\\cdot x\\cdot y^2}\\right)}^2=\\dfrac{x^6\\cdot {y}^{-4}}{4^2\\cdot x^2\\cdot y^4}=\\dfrac{x^6}{16\\cdot x^2\\cdot y^4\\cdot y^4}=\\dfrac{{x}^{^{6-2}}}{16\\cdot {y}^{^{4+4}}}=\\dfrac{x^4}{16y^8}[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p><span style=\"color: #000000;\">The following video provides more examples of simplifying expressions using the power of a quotient and other exponent rules.<\/span><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-9\" title=\"Simplify Expressions Using Exponent Rules (Power of a Quotient)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/BoBe31pRxFM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>The video below works through some examples of simplifying expressions that contain powers and negative exponents.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-10\" title=\"Ex 4:  Simplify Expressions with Negative Exponents\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/OYx7A0h2DII?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<h2 id=\"pf\" style=\"text-align: center;\"><span style=\"text-decoration: underline;\">Polynomial Functions and Expressions<\/span><\/h2>\n<p>You may see a resemblance between expressions and polynomials which we have been studying in this course. \u00a0Polynomials are a special sub-group of mathematical expressions and equations. A polynomial is an expression consisting of the sum or difference of terms in which each term is a\u00a0real\u00a0number, a variable, or the product of a\u00a0real\u00a0number and variable(s) with non-negative integer exponent(s). Non negative integers are\u00a0[latex]0, 1, 2, 3, 4[\/latex], &#8230;<br \/>\nThe basic building block of a polynomial is a <b>monomial<\/b>. A monomial is one term and can be a number, a variable, or the product of a number and variable(s) with an exponent. The number part of the term is called the <b>coefficient<\/b>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/06\/01183539\/image003.jpg\" alt=\"The expression 6x to the power of 3. 6 is the coefficient, x is the variable, and the power of 3 is the exponent.\" width=\"183\" height=\"82\" \/><\/p>\n<p>A polynomial containing two terms, such as [latex]2x - 9[\/latex], is called a <strong>binomial<\/strong>. A polynomial containing three terms, such as [latex]-3{x}^{2}+8x - 7[\/latex], is called a <strong>trinomial<\/strong>. We can find the <strong>degree<\/strong> of a single variable polynomial by identifying the highest power of the variable that occurs in the polynomial. You will discuss the degree of multivariable polynomials in later courses. The term with the highest degree is called the <strong>leading term<\/strong> because it is usually written first. The coefficient of the leading term is called the <strong>leading coefficient<\/strong>. When a polynomial is written so that the powers on a specified variable are descending, meaning the power of the term decreases for each succeeding term, we say that it is in standard form. It is important to note that polynomials only have integer exponents.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2550 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/15150341\/Screen-Shot-2016-07-15-at-8.03.13-AM-300x150.png\" alt=\"4x^3 - 9x^2 + 6x, with the text &quot;degree = 3&quot; and an arrow pointing at the exponent on x^3, and the text &quot;leading term =4&quot; with an arrow pointing at the 4.\" width=\"504\" height=\"252\" \/><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>For the following polynomials, identify the degree, the leading term, and the leading coefficient.<\/p>\n<ol>\n<li>[latex]3+2{x}^{2}-4{x}^{3}[\/latex]<\/li>\n<li>[latex]5{t}^{5}-2{t}^{3}+7t[\/latex]<\/li>\n<li>[latex]6p-{p}^{3}-2[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q753071\">Show Solution<\/span><\/p>\n<div id=\"q753071\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>The highest power of [latex]x[\/latex] is\u00a0[latex]3[\/latex], so the degree is\u00a0[latex]3[\/latex].\n<ul>\n<li>The leading term is the term containing that degree, [latex]-4{x}^{3}[\/latex].<\/li>\n<li>The leading coefficient is the coefficient of that term, [latex]-4[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li>The highest power of [latex]t[\/latex] is [latex]5[\/latex], so the degree is [latex]5[\/latex].\n<ul>\n<li>The leading term is the term containing that degree, [latex]5{t}^{5}[\/latex].<\/li>\n<li>The leading coefficient is the coefficient of that term, [latex]5[\/latex].<\/li>\n<\/ul>\n<\/li>\n<li>The highest power of [latex]p[\/latex] is [latex]3[\/latex], so the degree is [latex]3[\/latex].\n<ul>\n<li>The leading term is the term containing that degree, [latex]-{p}^{3}[\/latex].<\/li>\n<li>The leading coefficient is the coefficient of that term, [latex]-1[\/latex].<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>In the following video, we will identify the terms, leading coefficient, and degree of a polynomial.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-11\" title=\"Ex:  Intro to Polynomials in One Variable\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/3u16B2PN9zk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Add and Subtract Polynomials<\/h2>\n<p>Recall from previous courses that we can add and subtract polynomials by combining like terms which are terms that contain the same variables raised to the same exponents. For example, [latex]5{x}^{2}[\/latex] and [latex]-2{x}^{2}[\/latex] are like terms and can be added to get [latex]3{x}^{2}[\/latex], but [latex]3x[\/latex] and [latex]3{x}^{2}[\/latex] are not like terms; therefore, they cannot be added.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the sum.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(12{x}^{2}+9x - 21\\right)+\\left(4{x}^{3}+8{x}^{2}-5x+20\\right)[\/latex]<\/p>\n<p style=\"text-align: left;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q222892\">Show Solution<\/span><\/p>\n<div id=\"q222892\" class=\"hidden-answer\" style=\"display: none\">\n<p>You can write one polynomial below the other, making sure to line up the like terms. Notice that the first polynomial does not have a [latex]x^3[\/latex] term.<\/p>\n<p>&nbsp;<\/p>\n<p>[latex]0{x}^{3}+12{x}^{2}+9x - 21\\\\ 4{x}^{3}+8{x}^{2}\\hspace{2mm}-5x+20[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: left;\">Combine like terms, paying close attention to the signs.<\/p>\n<p>&nbsp;<\/p>\n<p>[latex]\\hspace{15mm}12{x}^{2}+9x - 21\\\\ \\underline{+4{x}^{3}+8{x}^{2}-5x+20}\\\\ \\hspace{3mm}4{x}^{3}+20{x}^{2}+4x-1[\/latex]<\/p>\n<p style=\"text-align: left;\"><\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>When you subtract polynomials, you will still be looking for like terms to combine, but you will need to pay attention to the sign of the terms you are combining. In the following example, we will show how to distribute the negative sign to each term of a polynomial that is being subtracted from another.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the difference.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(7{x}^{4}-{x}^{2}+6x+1\\right)-\\left(5{x}^{3}-2{x}^{2}+3x+2\\right)[\/latex]<\/p>\n<p style=\"text-align: left;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q279648\">Show Solution<\/span><\/p>\n<div id=\"q279648\" class=\"hidden-answer\" style=\"display: none\">\n<p>Since we are subtracting all of the second polynomial from the first polynomial, start by distributing the negative through the parentheses of the second polynomial. This will change the sign of each term to its opposite and you will have:<\/p>\n<p>&nbsp;<\/p>\n<p>[latex]\\left(7{x}^{4}-{x}^{2}+6x+1\\right)-5{x}^{3}+2{x}^{2}-3x-2[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>Write the polynomials so that the like terms are lined up. Notice that the [latex]{x}^{3}[\/latex] term is missing from the first polynomial and the [latex]{x}^{4}[\/latex] term is missing from the second polynomial. Then combine the like terms together.<\/p>\n<p>&nbsp;<\/p>\n<p>[latex]\\hspace{5mm} 7{x}^{4}+0{x}^{3}-\\hspace{2mm}{x}^{2}+6x+1\\\\ \\underline{+0{x}^{4}-5{x}^{3}+2{x}^{2}-3x-2}\\\\ \\hspace{3mm}7{x}^{4}-5{x}^{3}+\\hspace{3mm}{x}^{2}+3x-1[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>*Note that finding the difference between two polynomials is the same as adding the opposite of the second polynomial to the first.<\/p>\n<p style=\"text-align: left;\"><\/div>\n<\/div>\n<\/div>\n<p>In the following video, we show more examples of adding and subtracting polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-12\" title=\"Ex:  Adding and Subtracting Polynomials\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/jiq3toC7wGM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Multiplying Polynomials<\/h2>\n<p><span style=\"background-color: #ffffff;\">Multiplying polynomials is a bit more challenging than adding and subtracting polynomials. We must use the distributive property to multiply each term in the first polynomial by each term in the second polynomial. We then combine like terms.<\/span><\/p>\n<p>The following video will provide you with examples of using the distributive property to find the product of\u00a0monomials and polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-13\" title=\"Ex:  Multiplying Using the Distributive Property\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/bwTmApTV_8o?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Multiplying Two Binomials<\/h2>\n<p>You can use the distributive property when multiplying two binomials. In other words, multiply each term in the first binomial by each term in the second.<\/p>\n<div class=\"textbox exercises\">\n<h3>EXAMPLE<\/h3>\n<p>Simplify. [latex](x+4)(x-2)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q101118\">Show Solution<\/span><\/p>\n<div id=\"q101118\" class=\"hidden-answer\" style=\"display: none\">\n<p>Distribute the [latex]x[\/latex] over [latex](x-2)[\/latex], then distribute the [latex]4[\/latex] over [latex](x-2)[\/latex].<\/p>\n<p>[latex]\\begin{align}  \\require{color}  &= x(x-2)+4(x-2)\\\\  &= {x}^{2}-2x+4x-8 &&\\color{blue}{\\textsf{multiply}}\\\\  &= {x}^{2}+2x-8 &&\\color{blue}{\\textsf{combine like terms}}\\\\  \\end{align}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h2>Using FOIL to Multiply Binomials<\/h2>\n<p>The acronym FOIL (First, Outer, Inner, Last) is a memory device to multiply two binomials. It is called the FOIL method because we multiply the<\/p>\n<p style=\"text-align: center;\"><strong>F<\/strong>irst terms,\u00a0<strong>O<\/strong>uter terms,\u00a0<strong>I<\/strong>nner terms, and\u00a0<strong>L<\/strong>ast terms.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"data:image\/png;base64,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\" width=\"611\" height=\"516\" alt=\"image\" \/><\/p>\n<p>The FOIL method arises out of the distributive property. We are simply multiplying each term of the first binomial by each term of the second binomial and then combining like terms. <strong>FOIL method only works when multiplying a binomial by another binomial.<\/strong><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Use FOIL to find the product. [latex](2x-18)(3x+3)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q787670\">Show Solution<\/span><\/p>\n<div id=\"q787670\" class=\"hidden-answer\" style=\"display: none\">\n<p>Find the product of the first terms.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200225\/CNX_CAT_Figure_01_04_004.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting 2 x and 3 x. On right is equation: 2 x times 3 x = 6 x squared.\" width=\"487\" height=\"52\" \/><\/p>\n<p>Find the product of the outer terms.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200227\/CNX_CAT_Figure_01_04_005.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting 2 x in first expression and plus 3 in second expression. On right is equation:  2 x times 3 = 6 x.\" width=\"487\" height=\"52\" \/><\/p>\n<p>Find the product of the inner terms.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200228\/CNX_CAT_Figure_01_04_006.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting negative 18 and 3 x. On right is equation: negative 18 times 3 x = negative 54 x.\" width=\"487\" height=\"52\" \/><\/p>\n<p>Find the product of the last terms.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/924\/2015\/09\/25200229\/CNX_CAT_Figure_01_04_007.jpg\" alt=\"Expressions 2 x - 18 and 3 x plus 3. Arrows above expression connecting negative 18 and plus 3. On right is equation: negative 18 times 3 = negative 54.\" width=\"487\" height=\"52\" \/><br \/>\n[latex]\\begin{align}  \\require{color}  &= 6{x}^{2}+6x - 54x - 54 \\\\ &= 6{x}^{2}-48x - 54 &&\\color{blue}{\\text{combine like terms}}\\end{align}[\/latex]\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video, we show an example of how to use the FOIL method to multiply two binomials. Remember that the FOIL method is only used when multiplying two binomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-14\" title=\"Multiply Binomials Using the FOIL Acronym\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/_MrdEFnXNGA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Using the Box Method to Multiply Polynomials<\/h2>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Another method you can use to multiply binomials is the Box Method, where you can use a table to organize the terms as shown below. Let&#8217;s use the Box Method to multiply [latex](4x-5)[\/latex] and [latex](2x+7)[\/latex]. Write one polynomial factor across the top and the other down the side. For each box in the table, multiply the term for that row by the term for that column. Then combine like terms to simplify. Notice that we need to keep the sign on each term when we write it in the table.<\/span><\/h3>\n<p>&nbsp;<\/p>\n<table style=\"width: 30%; border: 1px solid black;\" summary=\"A table with 3 rows and 3 columns. The first entry of the first row is empty, the second entry reads: four times x The third entry reads: negative 5. The first entry of the second row is labeled: two times x. The second entry reads:eight x squared. The third entry reads: negative ten times x. The first entry of the third row reads: positive seven. The second entry reads: twenty eight times x. The third entry reads: negative thirty five.\">\n<thead>\n<tr style=\"height: 14px;\">\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\"><\/td>\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]4x[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-5[\/latex]<\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"width: 138.4375px; height: 19px; border: 1px solid #999999;\">[latex]2x[\/latex]<\/td>\n<td style=\"width: 174.53125px; height: 19px; border: 1px solid #999999;\">[latex]8{x}^{2}[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 19px; border: 1px solid #999999;\">[latex]-10x[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\">[latex]+7[\/latex]<\/td>\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]28x[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-35[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{align}  \\require{color}  (4x-5)(2x+7) &= 8{x}^{2}-10x +28x - 35 \\\\ &= 8{x}^{2}+18x - 35 &&\\color{blue}{\\text{combine like terms}}\\end{align}[\/latex]<\/p>\n<h2>Multiplying a Binomial with a Trinomial<\/h2>\n<p>Another type of polynomial multiplication problem is the product of a binomial and trinomial. Although the FOIL method cannot be used since there are more than two terms in a trinomial, you still use the distributive property to organize the individual products. Using the distributive property, each term in the binomial must be multiplied by each of the terms in the trinomial. For this example, we will show you two ways to organize all of the terms that result from multiplying polynomials with more than two terms. The most important part of the process is finding a way to organize terms.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the product using the Distributive Property. \u00a0[latex]\\left(3x-6\\right)\\left(5x^{2}+3x+10\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q637359\">Show Solution<\/span><\/p>\n<div id=\"q637359\" class=\"hidden-answer\" style=\"display: none\">\n<p style=\"text-align: left;\">Distribute the trinomial to each term in the binomial.<br \/>\n[latex]\\begin{align}  \\require{color}  &= 3x\\left(5x^{2}+3x+10\\right)-6\\left(5x^{2}+3x+10\\right)&&\\color{blue}{\\textsf{use the distributive property}}\\\\  &= 3x\\left(5x^{2}\\right)+3x\\left(3x\\right)+3x\\left(10\\right)-6\\left(5x^{2}\\right)-6\\left(3x\\right)-6\\left(10\\right) && \\color{blue}{\\textsf{multiply}}\\\\  &= 15x^{3}+9x^{2}+30x-30x^{2}-18x-60\\\\  &= 15x^{3}+\\left(9x^{2}-30x^{2}\\right)+\\left(30x-18x\\right)-60 && \\color{blue}{\\textsf{group like terms}}\\\\  &=15x^{3}-21x^{2}+12x-60 && \\color{blue}{\\textsf{combine like terms}}\\\\ \\end{align}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>We will now rework this example using the Box Method. The Box Method is good to use when you are multiplying a binomial by a trinomial because it can help you keep track of all of the terms involved.<\/p>\n<div class=\"textbox exercises\">\n<h3>ExAMPLE<\/h3>\n<p>Find the product using the Box Method. [latex](3x-6)(5{x}^{2}+3x+10)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q530295\">Show Solution<\/span><\/p>\n<div id=\"q530295\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"width: 30%; border: 1px solid black;\" summary=\"A table with 3 rows and 4 columns. The first entry of the first row is empty, the second entry reads: five times x squared, the third entry reads: three times x, the fourth entry reads: positive ten. The first entry of the second row is labeled: three times x. The second entry reads: fifteen x cubed. The third entry reads: nine x squared. The fourth entry reads: thirty times x. The first entry of the third row reads: negative six. The second entry reads: negative thirty x squared. The third entry reads: negative eighteen times x. The fourth entry reads: negative sixty. The first entry of the fourth row is labeled: negative six. The second entry reads: negative thirty x squared. The third entry reads: negative eighteen times x. The fourth entry reads: negative sixty.\">\n<thead>\n<tr style=\"height: 14px;\">\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\"><\/td>\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]5x^2[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]+3x[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]+10[\/latex]<\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"width: 138.4375px; height: 19px; border: 1px solid #999999;\">[latex]3x[\/latex]<\/td>\n<td style=\"width: 174.53125px; height: 19px; border: 1px solid #999999;\">[latex]15{x}^{3}[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 19px; border: 1px solid #999999;\">[latex]9x^2[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]30x[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\">[latex]-6[\/latex]<\/td>\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]-30x^2[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-18x[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-60[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Let&#8217;s line up the like terms on top of each other so that it is easier to combine the like terms together.<\/p>\n<p>[latex]15x^{3}+9x^{2}+30x\\\\  \\underline{\\hspace{1cm}-30x^{2}-18x-60}\\\\  15x^{3}-21x^{2}+12x-60[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<h3><span style=\"font-size: 1rem; font-weight: normal; orphans: 1; text-align: initial; widows: 2; color: #373d3f;\">Let&#8217;s look at another example where we are multiplying a binomial with a trinomial. Pay attention to the signs on the terms. Forgetting a negative sign is the easiest mistake to make in this case.<\/span><\/h3>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the product using the Distributive Property.<\/p>\n<p>[latex]\\left(2x+1\\right)\\left(3{x}^{2}-x+4\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q485882\">Show Solution<\/span><\/p>\n<div id=\"q485882\" class=\"hidden-answer\" style=\"display: none\">\n[latex]\\begin{align}\\require{color}  &= 2x\\left(3{x}^{2}-x+4\\right)+1\\left(3{x}^{2}-x+4\\right) && \\color{blue}{\\textsf{use the distributive property}}\\\\  &= \\left(6{x}^{3}-2{x}^{2}+8x\\right)+\\left(3{x}^{2}-x+4\\right) && \\color{blue}{\\textsf{multiply}}\\\\  &= 6{x}^{3}+\\left(-2{x}^{2}+3{x}^{2}\\right)+\\left(8x-x\\right)+4 && \\color{blue}{\\textsf{group like terms}}\\\\  &= 6{x}^{3}+{x}^{2}+7x+4 && \\color{blue}{\\textsf{combine like terms}}\\end{align}[\/latex]\n<\/div>\n<\/div>\n<\/div>\n<p>We will rework the above example using the Box Method<\/p>\n<div class=\"textbox exercises\">\n<h3>ExAMPLE<\/h3>\n<p>Find the product using the Box Method.<\/p>\n<p>[latex]\\left(2x+1\\right)\\left(3{x}^{2}-x+4\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q320112\">Show Solution<\/span><\/p>\n<div id=\"q320112\" class=\"hidden-answer\" style=\"display: none\">\n<table style=\"width: 30%;\" summary=\"A table with 3 rows and 4 columns. The first entry of the first row is empty, the others are labeled: three times x squared, negative x, and positive four. The first entry of the second row is labeled: two times x. The second entry reads: six times x cubed. The third entry reads: negative two times x squared. The fourth entry reads: eight times x. The first entry of the third row reads: positive one. The second entry reads: three times x squared. The third entry reads: negative x. The fourth entry reads: four.\">\n<thead>\n<tr style=\"height: 14px;\">\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\"><\/td>\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]3x^2[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-x[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]+4[\/latex]<\/td>\n<\/tr>\n<\/thead>\n<tbody>\n<tr style=\"height: 19px;\">\n<td style=\"width: 138.4375px; height: 19px; border: 1px solid #999999;\">[latex]2x[\/latex]<\/td>\n<td style=\"width: 174.53125px; height: 19px; border: 1px solid #999999;\">[latex]6{x}^{3}[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 19px; border: 1px solid #999999;\">[latex]-2x^2[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]8x[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 138.4375px; height: 14px; border: 1px solid #999999;\">[latex]+1[\/latex]<\/td>\n<td style=\"width: 174.53125px; height: 14px; border: 1px solid #999999;\">[latex]3x^2[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]-x[\/latex]<\/td>\n<td style=\"width: 152.46875px; height: 14px; border: 1px solid #999999;\">[latex]4[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Let&#8217;s line up the like terms on top of each other so that it is easier to combine the like terms together.<\/p>\n<p>[latex]6x^{3}-2x^{2}+8x\\\\  \\underline{\\hspace{13mm}3x^{2}\\hspace{2mm}-x+4}\\\\  6x^{3}\\hspace{2mm}+x^{2}+7x+4[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video, we show more examples of multiplying polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-15\" title=\"(New Version Available) Polynomial Multiplication Involving Binomials and Trinomials\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/bBKbldmlbqI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-147\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Ex: Multiplying Using the Distributive Property. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/bwTmApTV_8o\">https:\/\/youtu.be\/bwTmApTV_8o<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Multiply Binomials Using An Area Model and Using Repeated Distribution. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/u4Hgl0BrUlo\">https:\/\/youtu.be\/u4Hgl0BrUlo<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Revision and Adaptation. <strong>Provided by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Multiply Binomials Using the FOIL Acronym. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/_MrdEFnXNGA\">https:\/\/youtu.be\/_MrdEFnXNGA<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>College Algebra. <strong>Authored by<\/strong>: Abramson, Jay, et al.. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\">http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at: http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface<\/li><li>Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/dm-opentext\">http:\/\/nrocnetwork.org\/dm-opentext<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Adding and Subtracting Polynomials. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/jiq3toC7wGM\">https:\/\/youtu.be\/jiq3toC7wGM<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Polynomial Multiplication Involving Binomials and Trinomials. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) . <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/bBKbldmlbqI\">https:\/\/youtu.be\/bBKbldmlbqI<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":395986,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"College Algebra\",\"author\":\"Abramson, Jay, et al.\",\"organization\":\"\",\"url\":\"http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at: http:\/\/cnx.org\/contents\/9b08c294-057f-4201-9f48-5d6ad992740d@3.278:1\/Preface\"},{\"type\":\"original\",\"description\":\"Ex: Multiplying Using the Distributive Property\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/bwTmApTV_8o\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Multiply Binomials Using An Area Model and Using Repeated Distribution\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/u4Hgl0BrUlo\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 11: Exponents and Polynomials, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology\",\"url\":\"http:\/\/nrocnetwork.org\/dm-opentext\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Multiply Binomials Using the FOIL Acronym\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/_MrdEFnXNGA\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Adding and Subtracting Polynomials\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/jiq3toC7wGM\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Polynomial Multiplication Involving Binomials and Trinomials\",\"author\":\"James Sousa (Mathispower4u.com) \",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/bBKbldmlbqI\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"a1f3dd5f-05ed-4622-9a46-74c3ba568cd8","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-147","chapter","type-chapter","status-publish","hentry"],"part":143,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/chapters\/147","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/wp\/v2\/users\/395986"}],"version-history":[{"count":150,"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/chapters\/147\/revisions"}],"predecessor-version":[{"id":2113,"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/chapters\/147\/revisions\/2113"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/parts\/143"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/chapters\/147\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/wp\/v2\/media?parent=147"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=147"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/wp\/v2\/contributor?post=147"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-interalgebra\/wp-json\/wp\/v2\/license?post=147"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}