{"id":4509,"date":"2017-06-07T18:50:10","date_gmt":"2017-06-07T18:50:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-simplify-expressions-with-real-numbers\/"},"modified":"2017-08-24T23:24:49","modified_gmt":"2017-08-24T23:24:49","slug":"read-simplify-expressions-with-real-numbers","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/aacc-collegealgebrafoundations\/chapter\/read-simplify-expressions-with-real-numbers\/","title":{"raw":"Simplify Expressions, Combine Like Terms, &amp; Order of Operations With Real Numbers","rendered":"Simplify Expressions, Combine Like Terms, &amp; Order of Operations With Real Numbers"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Objectives<\/h3>\r\n<ul>\r\n \t<li>Simplify expressions with real numbers\r\n<ul>\r\n \t<li>Recognize and combine like terms in an expression<\/li>\r\n \t<li>Use the order of operations to simplify expressions<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/div>\r\n<h2>Introduction<\/h2>\r\nSome important terminology before we begin:\r\n<ul>\r\n \t<li><strong>operations\/operators:<\/strong>\u00a0In mathematics we call things like multiplication, division, addition, and subtraction operations. \u00a0They are the verbs of the math world, doing work on numbers and variables. The symbols used to denote operations are called operators, such as [latex]+{, }-{, }\\times{, }\\div[\/latex]. As you learn more math, you will learn more operators.<\/li>\r\n \t<li><strong>term:\u00a0<\/strong>Examples of terms would be [latex]2x[\/latex] and [latex]-\\frac{3}{2}[\/latex] or [latex]a^3[\/latex]. Even lone integers can be a term, like 0.<\/li>\r\n \t<li><strong>expression:\u00a0A<\/strong>\u00a0mathematical expression is one that connects terms with mathematical operators.\u00a0For example \u00a0[latex]\\frac{1}{2}+\\left(2^2\\right)- 9\\div\\frac{6}{7}[\/latex] is an expression.<\/li>\r\n<\/ul>\r\n<h2><\/h2>\r\n<h2>Combining Like Terms<\/h2>\r\nOne way we can simplify expressions is to combine like terms. <strong>Like terms<\/strong> are terms where the variables match exactly (exponents included). Examples of like terms would be [latex]5xy[\/latex] and [latex]-3xy[\/latex] or [latex]8a^2b[\/latex] and [latex]a^2b[\/latex] or [latex]-3[\/latex] and [latex]8[\/latex]. \u00a0If we have like terms we are\u00a0allowed to add (or subtract) the\u00a0numbers in front of the variables, then keep the variables the same. As we combine like terms we need to interpret subtraction signs as part of the following term. This means if we see a subtraction sign, we treat the following term like a negative term. The sign always stays with the term.\r\n\r\nThis is shown in the following examples:\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nCombine like terms: \u00a0[latex]5x-2y-8x+7y[\/latex]\r\n[reveal-answer q=\"730653\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"730653\"]\r\n\r\nThe like terms in this expression are:\r\n<p style=\"text-align: center;\">[latex]5x[\/latex] and [latex]-8x[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]-2y[\/latex] and [latex]-7y[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Note how we kept the sign in front of each term.<\/p>\r\n<p style=\"text-align: left;\">Combine like terms:<\/p>\r\n<p style=\"text-align: center;\">[latex]5x-8x = -3x[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]-2y-7y = -9y[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Note how signs become operations when you combine like terms.<\/p>\r\n<p style=\"text-align: left;\">Simplified Expression:<\/p>\r\n<p style=\"text-align: center;\">[latex]5x-2y-8x+7y=-3x-9y[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\nIn the following video you will be shown how to combine like terms using the idea of the distributive property. \u00a0Note that this is a different method than is shown in the written examples on this page, but it obtains the same result.\r\n\r\nhttps:\/\/youtu.be\/JIleqbO8Tf0\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nCombine like terms: \u00a0[latex]x^2-3x+9-5x^2+3x-1[\/latex]\r\n\r\n[reveal-answer q=\"730650\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"730650\"]\r\n\r\nThe like terms in this expression are:\r\n<p style=\"text-align: center;\">[latex]x^2[\/latex] and [latex]-5x^2[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]-3x[\/latex] and [latex]3x[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]9[\/latex] and [latex]-1[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Combine like terms:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}x^2-5x^2 = -4x^2\\\\-3x+3x=0\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\9-1=8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[\/hidden-answer]<\/p>\r\n\r\n<\/div>\r\nIn the video that follows, you will be shown another example of\u00a0combining like terms. \u00a0Pay attention to why you are not able to combine all three terms in the example.\r\n\r\nhttps:\/\/youtu.be\/b9-7eu29pNM\r\n<h2>Order of Operations<\/h2>\r\nYou may or may not recall the order of operations for applying several mathematical operations to one expression. Just as it is a social convention for us to drive on the right-hand side of the road, the order of operations is a set of conventions used to provide order when you are required to use several mathematical operations for one expression. The graphic below depicts the order in which mathematical operations are performed.\r\n\r\n[caption id=\"attachment_5107\" align=\"aligncenter\" width=\"600\"]<img class=\"wp-image-5107\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/24232350\/orderofoperations.png\" alt=\"Order of operations. Step 1, grouping. Step 2, exponents and roots. Step 3, multiply and divide from left to right. Step 4, add and subtract from left to right.\" width=\"600\" height=\"381\" \/> Order of Operations[\/caption]\r\n\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSimplify [latex]7\u20135+3\\cdot8[\/latex].\r\n\r\n[reveal-answer q=\"987816\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"987816\"]According to the order of operations, multiplication comes before addition and subtraction.\r\n\r\nMultiply [latex]3\\cdot8[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}7\u20135+3\\cdot8\\\\7\u20135+24\\end{array}[\/latex]<\/p>\r\nNow, add and subtract from left to right. [latex]7\u20135[\/latex] comes first.\r\n<p style=\"text-align: center;\">[latex]2+24[\/latex].<\/p>\r\n<p style=\"text-align: left;\">Finally, add.<\/p>\r\n<p style=\"text-align: center;\">[latex]2+24=26[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]7\u20135+3\\cdot8=26[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following example, you will be shown how to simplify an expression that contains both multiplication and subtraction using the order of operations.\r\n\r\nhttps:\/\/youtu.be\/yFO_0dlfy-w\r\n\r\nWhen you are applying the order of operations to expressions that contain fractions, decimals, and negative numbers, you will need to recall how to do these computations as well.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSimplify [latex]3\\cdot\\frac{1}{3}-8\\div\\frac{1}{4}[\/latex].\r\n\r\n[reveal-answer q=\"265256\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"265256\"]According to the order of operations, multiplication and division come before addition and subtraction. Sometimes it helps to add parentheses to help you know what comes first, so let's put parentheses around the multiplication and division since it will come before the subtraction.\r\n<p style=\"text-align: center;\">[latex]3\\cdot\\frac{1}{3}-8\\div\\frac{1}{4}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Multiply [latex] 3\\cdot \\frac{1}{3}[\/latex] first.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\left(3\\cdot\\frac{1}{3}\\right)-\\left(8\\div\\frac{1}{4}\\right)\\\\\\text{}\\\\=\\left(1\\right)-\\left(8\\div \\frac{1}{4}\\right)\\end{array}[\/latex]<\/p>\r\nNow, divide [latex]8\\div\\frac{1}{4}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}8\\div\\frac{1}{4}=\\frac{8}{1}\\cdot\\frac{4}{1}=32\\\\\\text{}\\\\1-32\\end{array}[\/latex]<\/p>\r\nSubtract.\r\n<p style=\"text-align: center;\">[latex]1\u201332=\u221231[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex] 3\\cdot \\frac{1}{3}-8\\div \\frac{1}{4}=-31[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video you are shown how to use the order of operations to simplify an expression that contains multiplication, division, and subtraction with terms that contain fractions.\r\n\r\nhttps:\/\/youtu.be\/yqp06obmcVc\r\n<h2>Exponents<\/h2>\r\nWhen you are evaluating expressions, you will sometimes see exponents used to represent repeated multiplication. Recall that an expression such as [latex]7^{2}[\/latex]\u00a0is <strong>exponential notation<\/strong> for [latex]7\\cdot7[\/latex]. (Exponential notation has two parts: the <strong>base<\/strong> and the <strong>exponent<\/strong> or the <strong>power<\/strong>. In [latex]7^{2}[\/latex], 7 is the base and 2 is the exponent; the exponent determines how many times the base is multiplied by itself.)\r\n\r\nExponents are a way to represent repeated multiplication; the order of operations places it <i>before <\/i>any other multiplication, division, subtraction, and addition is performed.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSimplify [latex]3^{2}\\cdot2^{3}[\/latex].\r\n\r\n[reveal-answer q=\"360237\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"360237\"]This problem has exponents and multiplication in it. According to the order of operations, simplifying\u00a0[latex]3^{2}[\/latex]\u00a0and [latex]2^{3}[\/latex]\u00a0comes before multiplication.\r\n<p style=\"text-align: center;\">[latex]3^{2}\\cdot2^{3}[\/latex]<\/p>\r\n[latex] {{3}^{2}}[\/latex] is [latex]3\\cdot3[\/latex], which equals 9.\r\n<p style=\"text-align: center;\">[latex] 9\\cdot {{2}^{3}}[\/latex]<\/p>\r\n[latex] {{2}^{3}}[\/latex] is [latex]2\\cdot2\\cdot2[\/latex], which equals 8.\r\n<p style=\"text-align: center;\">[latex] 9\\cdot 8[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex] 9\\cdot 8=72[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex] {{3}^{2}}\\cdot {{2}^{3}}=72[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the video that follows, an expression with exponents on its terms is simplified using the order of operations.\r\n\r\nhttps:\/\/youtu.be\/JjBBgV7G_Qw\r\n<h2>Grouping Symbols<\/h2>\r\nGrouping symbols such as parentheses ( ), brackets [ ], braces[latex] \\displaystyle \\left\\{ {} \\right\\}[\/latex], and fraction bars can be used to further control the order of the four arithmetic operations.\u00a0The rules of the order of operations require computation within grouping symbols to be completed first, even if you are adding or subtracting within the grouping symbols and you have multiplication outside the grouping symbols. After computing within the grouping symbols, divide or multiply from left to right and then subtract or add from left to right.\u00a0When there are grouping symbols within grouping symbols, calculate from the inside to the outside. That is, begin simplifying within the innermost grouping symbols first.\r\n\r\nRemember that parentheses can also be used to show multiplication. In the example that follows, both uses of parentheses\u2014as a way to represent a group, as well as a way to express multiplication\u2014are shown.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nSimplify [latex]\\left(3+4\\right)^{2}+\\left(8\\right)\\left(4\\right)[\/latex].\r\n\r\n[reveal-answer q=\"548490\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"548490\"]This problem has parentheses, exponents, multiplication, and addition in it. The first set of parentheses is a grouping symbol. The second set indicates multiplication.\r\n\r\nGrouping symbols are handled first. Add numbers in parentheses.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}(3+4)^{2}+(8)(4)\\\\(7)^{2}+(8)(4)\\end{array}[\/latex]<\/p>\r\nSimplify\u00a0[latex]7^{2}[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}7^{2}+(8)(4)\\\\49+(8)(4)\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Multiply.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}49+(8)(4)\\\\49+(32)\\end{array}[\/latex]<\/p>\r\n<p style=\"text-align: left;\">Add.<\/p>\r\n<p style=\"text-align: center;\">[latex]49+32=81[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex](3+4)^{2}+(8)(4)=81[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nSimplify \u00a0[latex]4\\cdot{\\frac{3[5+{(2 + 3)}^2]}{2}}[\/latex]\r\n[reveal-answer q=\"358226\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"358226\"]\r\n\r\nThere are brackets and parentheses in this problem. Compute inside the innermost grouping symbols first.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}4\\cdot{\\frac{3[5+{(2 + 3)}^2]}{2}}\\\\\\text{ }\\\\=4\\cdot{\\frac{3[5+{(5)}^2]}{2}}\\end{array}[\/latex]<\/p>\r\nThen apply the exponent\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}4\\cdot{\\frac{3[5+{(5)}^2]}{2}}\\\\\\text{}\\\\=4\\cdot{\\frac{3[5+25]}{2}}\\\\\\text{ }\\\\=4\\cdot{\\frac{3[30]}{2}}\\end{array}[\/latex]<\/p>\r\nThen simplify the fraction\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}4\\cdot{\\frac{3[30]}{2}}\\\\\\text{}\\\\=4\\cdot{\\frac{90}{2}}\\\\\\text{ }\\\\=4\\cdot{45}\\\\\\text{ }\\\\=180\\end{array}[\/latex]<\/p>\r\n\r\n<h4 style=\"text-align: left;\">Answer<\/h4>\r\n[latex]4\\cdot{\\frac{3[5+{(2 + 3)}^2]}{2}}=180[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, you are shown how to use the order of operations to simplify an expression with grouping symbols, exponents, multiplication, and addition.\r\n\r\nhttps:\/\/youtu.be\/EMch2MKCVdA\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Think About It<\/h3>\r\nThese problems are very similar to the examples given above. How are they different and what tools do you need to simplify them?\r\n\r\na) Simplify\u00a0[latex]\\left(1.5+3.5\\right)\u20132\\left(0.5\\cdot6\\right)^{2}[\/latex].\u00a0This problem has parentheses, exponents, multiplication, subtraction, and addition in it, as well as decimals instead of integers.\r\n\r\nUse the box below to write down a few thoughts about how you would simplify this expression with decimals and grouping symbols.\r\n\r\n[practice-area rows=\"2\"][\/practice-area]\r\n<p class=\"p1\">[reveal-answer q=\"680970\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"680970\"]\r\nGrouping symbols are handled first. Add numbers in the first set of parentheses.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}(1.5+3.5)\u20132(0.5\\cdot6)^{2}\\\\5\u20132(0.5\\cdot6)^{2}\\end{array}[\/latex]<\/p>\r\nMultiply numbers in the second set of parentheses.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}5\u20132(0.5\\cdot6)^{2}\\\\5\u20132(3)^{2}\\end{array}[\/latex]<\/p>\r\nEvaluate exponents.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}5\u20132(3)^{2}\\\\5\u20132\\cdot9\\end{array}[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}5\u20132\\cdot9\\\\5\u201318\\end{array}[\/latex]<\/p>\r\nSubtract.\r\n<p style=\"text-align: center;\">[latex]5\u201318=\u221213[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex](1.5+3.5)\u20132(0.5\\cdot6)^{2}=\u221213[\/latex]\r\n\r\n[\/hidden-answer]\r\n<p class=\"p1\">b) Simplify [latex] {{\\left( \\frac{1}{2} \\right)}^{2}}+{{\\left( \\frac{1}{4} \\right)}^{3}}\\cdot \\,32[\/latex].<\/p>\r\nUse the box below to write down a few thoughts about how you would simplify this expression with fractions and grouping symbols.\r\n\r\n[practice-area rows=\"2\"][\/practice-area]\r\n[reveal-answer q=\"680972\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"680972\"]\r\nThis problem has exponents, multiplication, and addition in it, as well as fractions instead of integers.\r\n\r\nAccording to the order of operations, simplify the terms with the exponents first, then multiply, then add.\r\n<p style=\"text-align: center;\">[latex]\\left(\\frac{1}{2}\\right)^{2}+\\left(\\frac{1}{4}\\right)^{3}\\cdot32[\/latex]<\/p>\r\nEvaluate: [latex]\\left(\\frac{1}{2}\\right)^{2}=\\frac{1}{2}\\cdot\\frac{1}{2}=\\frac{1}{4}[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}+\\left(\\frac{1}{4}\\right)^{3}\\cdot32[\/latex]<\/p>\r\nEvaluate: [latex]\\left(\\frac{1}{4}\\right)^{3}=\\frac{1}{4}\\cdot\\frac{1}{4}\\cdot\\frac{1}{4}=\\frac{1}{64}[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}+\\frac{1}{64}\\cdot32[\/latex]<\/p>\r\nMultiply.\r\n<p style=\"text-align: center;\">[latex] \\frac{1}{4}+\\frac{32}{64}[\/latex]<\/p>\r\nSimplify. [latex] \\frac{32}{64}=\\frac{1}{2}[\/latex], so you can add [latex] \\frac{1}{4}+\\frac{1}{2}[\/latex].\r\n<p style=\"text-align: center;\">[latex] \\frac{1}{4}+\\frac{1}{2}=\\frac{3}{4}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex] {{\\left( \\frac{1}{2} \\right)}^{2}}+{{\\left( \\frac{1}{4} \\right)}^{3}}\\cdot 32=\\frac{3}{4}[\/latex][\/hidden-answer]\r\n\r\n<\/div>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Objectives<\/h3>\n<ul>\n<li>Simplify expressions with real numbers\n<ul>\n<li>Recognize and combine like terms in an expression<\/li>\n<li>Use the order of operations to simplify expressions<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<h2>Introduction<\/h2>\n<p>Some important terminology before we begin:<\/p>\n<ul>\n<li><strong>operations\/operators:<\/strong>\u00a0In mathematics we call things like multiplication, division, addition, and subtraction operations. \u00a0They are the verbs of the math world, doing work on numbers and variables. The symbols used to denote operations are called operators, such as [latex]+{, }-{, }\\times{, }\\div[\/latex]. As you learn more math, you will learn more operators.<\/li>\n<li><strong>term:\u00a0<\/strong>Examples of terms would be [latex]2x[\/latex] and [latex]-\\frac{3}{2}[\/latex] or [latex]a^3[\/latex]. Even lone integers can be a term, like 0.<\/li>\n<li><strong>expression:\u00a0A<\/strong>\u00a0mathematical expression is one that connects terms with mathematical operators.\u00a0For example \u00a0[latex]\\frac{1}{2}+\\left(2^2\\right)- 9\\div\\frac{6}{7}[\/latex] is an expression.<\/li>\n<\/ul>\n<h2><\/h2>\n<h2>Combining Like Terms<\/h2>\n<p>One way we can simplify expressions is to combine like terms. <strong>Like terms<\/strong> are terms where the variables match exactly (exponents included). Examples of like terms would be [latex]5xy[\/latex] and [latex]-3xy[\/latex] or [latex]8a^2b[\/latex] and [latex]a^2b[\/latex] or [latex]-3[\/latex] and [latex]8[\/latex]. \u00a0If we have like terms we are\u00a0allowed to add (or subtract) the\u00a0numbers in front of the variables, then keep the variables the same. As we combine like terms we need to interpret subtraction signs as part of the following term. This means if we see a subtraction sign, we treat the following term like a negative term. The sign always stays with the term.<\/p>\n<p>This is shown in the following examples:<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Combine like terms: \u00a0[latex]5x-2y-8x+7y[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q730653\">Show Solution<\/span><\/p>\n<div id=\"q730653\" class=\"hidden-answer\" style=\"display: none\">\n<p>The like terms in this expression are:<\/p>\n<p style=\"text-align: center;\">[latex]5x[\/latex] and [latex]-8x[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]-2y[\/latex] and [latex]-7y[\/latex]<\/p>\n<p style=\"text-align: left;\">Note how we kept the sign in front of each term.<\/p>\n<p style=\"text-align: left;\">Combine like terms:<\/p>\n<p style=\"text-align: center;\">[latex]5x-8x = -3x[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]-2y-7y = -9y[\/latex]<\/p>\n<p style=\"text-align: left;\">Note how signs become operations when you combine like terms.<\/p>\n<p style=\"text-align: left;\">Simplified Expression:<\/p>\n<p style=\"text-align: center;\">[latex]5x-2y-8x+7y=-3x-9y[\/latex]<\/p>\n<p style=\"text-align: center;\"><\/div>\n<\/div>\n<\/div>\n<p>In the following video you will be shown how to combine like terms using the idea of the distributive property. \u00a0Note that this is a different method than is shown in the written examples on this page, but it obtains the same result.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Combining Like Terms\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JIleqbO8Tf0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Combine like terms: \u00a0[latex]x^2-3x+9-5x^2+3x-1[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q730650\">Show Solution<\/span><\/p>\n<div id=\"q730650\" class=\"hidden-answer\" style=\"display: none\">\n<p>The like terms in this expression are:<\/p>\n<p style=\"text-align: center;\">[latex]x^2[\/latex] and [latex]-5x^2[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]-3x[\/latex] and [latex]3x[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]9[\/latex] and [latex]-1[\/latex]<\/p>\n<p style=\"text-align: left;\">Combine like terms:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}x^2-5x^2 = -4x^2\\\\-3x+3x=0\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\\\9-1=8\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\end{array}[\/latex]<\/p>\n<p style=\"text-align: center;\"><\/div>\n<\/div>\n<\/div>\n<p>In the video that follows, you will be shown another example of\u00a0combining like terms. \u00a0Pay attention to why you are not able to combine all three terms in the example.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 2:  Combining Like Terms\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/b9-7eu29pNM?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Order of Operations<\/h2>\n<p>You may or may not recall the order of operations for applying several mathematical operations to one expression. Just as it is a social convention for us to drive on the right-hand side of the road, the order of operations is a set of conventions used to provide order when you are required to use several mathematical operations for one expression. The graphic below depicts the order in which mathematical operations are performed.<\/p>\n<div id=\"attachment_5107\" style=\"width: 610px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5107\" class=\"wp-image-5107\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/2011\/2017\/06\/24232350\/orderofoperations.png\" alt=\"Order of operations. Step 1, grouping. Step 2, exponents and roots. Step 3, multiply and divide from left to right. Step 4, add and subtract from left to right.\" width=\"600\" height=\"381\" \/><\/p>\n<p id=\"caption-attachment-5107\" class=\"wp-caption-text\">Order of Operations<\/p>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Simplify [latex]7\u20135+3\\cdot8[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q987816\">Show Solution<\/span><\/p>\n<div id=\"q987816\" class=\"hidden-answer\" style=\"display: none\">According to the order of operations, multiplication comes before addition and subtraction.<\/p>\n<p>Multiply [latex]3\\cdot8[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}7\u20135+3\\cdot8\\\\7\u20135+24\\end{array}[\/latex]<\/p>\n<p>Now, add and subtract from left to right. [latex]7\u20135[\/latex] comes first.<\/p>\n<p style=\"text-align: center;\">[latex]2+24[\/latex].<\/p>\n<p style=\"text-align: left;\">Finally, add.<\/p>\n<p style=\"text-align: center;\">[latex]2+24=26[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]7\u20135+3\\cdot8=26[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following example, you will be shown how to simplify an expression that contains both multiplication and subtraction using the order of operations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Simplify an Expression in the Form:  a-b+c*d\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/yFO_0dlfy-w?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>When you are applying the order of operations to expressions that contain fractions, decimals, and negative numbers, you will need to recall how to do these computations as well.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Simplify [latex]3\\cdot\\frac{1}{3}-8\\div\\frac{1}{4}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q265256\">Show Solution<\/span><\/p>\n<div id=\"q265256\" class=\"hidden-answer\" style=\"display: none\">According to the order of operations, multiplication and division come before addition and subtraction. Sometimes it helps to add parentheses to help you know what comes first, so let&#8217;s put parentheses around the multiplication and division since it will come before the subtraction.<\/p>\n<p style=\"text-align: center;\">[latex]3\\cdot\\frac{1}{3}-8\\div\\frac{1}{4}[\/latex]<\/p>\n<p style=\"text-align: left;\">Multiply [latex]3\\cdot \\frac{1}{3}[\/latex] first.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}\\left(3\\cdot\\frac{1}{3}\\right)-\\left(8\\div\\frac{1}{4}\\right)\\\\\\text{}\\\\=\\left(1\\right)-\\left(8\\div \\frac{1}{4}\\right)\\end{array}[\/latex]<\/p>\n<p>Now, divide [latex]8\\div\\frac{1}{4}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}8\\div\\frac{1}{4}=\\frac{8}{1}\\cdot\\frac{4}{1}=32\\\\\\text{}\\\\1-32\\end{array}[\/latex]<\/p>\n<p>Subtract.<\/p>\n<p style=\"text-align: center;\">[latex]1\u201332=\u221231[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]3\\cdot \\frac{1}{3}-8\\div \\frac{1}{4}=-31[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video you are shown how to use the order of operations to simplify an expression that contains multiplication, division, and subtraction with terms that contain fractions.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-4\" title=\"Simplify an Expression in the Form:  a*1\/b-c\/(1\/d)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/yqp06obmcVc?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Exponents<\/h2>\n<p>When you are evaluating expressions, you will sometimes see exponents used to represent repeated multiplication. Recall that an expression such as [latex]7^{2}[\/latex]\u00a0is <strong>exponential notation<\/strong> for [latex]7\\cdot7[\/latex]. (Exponential notation has two parts: the <strong>base<\/strong> and the <strong>exponent<\/strong> or the <strong>power<\/strong>. In [latex]7^{2}[\/latex], 7 is the base and 2 is the exponent; the exponent determines how many times the base is multiplied by itself.)<\/p>\n<p>Exponents are a way to represent repeated multiplication; the order of operations places it <i>before <\/i>any other multiplication, division, subtraction, and addition is performed.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Simplify [latex]3^{2}\\cdot2^{3}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q360237\">Show Solution<\/span><\/p>\n<div id=\"q360237\" class=\"hidden-answer\" style=\"display: none\">This problem has exponents and multiplication in it. According to the order of operations, simplifying\u00a0[latex]3^{2}[\/latex]\u00a0and [latex]2^{3}[\/latex]\u00a0comes before multiplication.<\/p>\n<p style=\"text-align: center;\">[latex]3^{2}\\cdot2^{3}[\/latex]<\/p>\n<p>[latex]{{3}^{2}}[\/latex] is [latex]3\\cdot3[\/latex], which equals 9.<\/p>\n<p style=\"text-align: center;\">[latex]9\\cdot {{2}^{3}}[\/latex]<\/p>\n<p>[latex]{{2}^{3}}[\/latex] is [latex]2\\cdot2\\cdot2[\/latex], which equals 8.<\/p>\n<p style=\"text-align: center;\">[latex]9\\cdot 8[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]9\\cdot 8=72[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]{{3}^{2}}\\cdot {{2}^{3}}=72[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the video that follows, an expression with exponents on its terms is simplified using the order of operations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-5\" title=\"Simplify an Expression in the Form:  a^n*b^m\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JjBBgV7G_Qw?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h2>Grouping Symbols<\/h2>\n<p>Grouping symbols such as parentheses ( ), brackets [ ], braces[latex]\\displaystyle \\left\\{ {} \\right\\}[\/latex], and fraction bars can be used to further control the order of the four arithmetic operations.\u00a0The rules of the order of operations require computation within grouping symbols to be completed first, even if you are adding or subtracting within the grouping symbols and you have multiplication outside the grouping symbols. After computing within the grouping symbols, divide or multiply from left to right and then subtract or add from left to right.\u00a0When there are grouping symbols within grouping symbols, calculate from the inside to the outside. That is, begin simplifying within the innermost grouping symbols first.<\/p>\n<p>Remember that parentheses can also be used to show multiplication. In the example that follows, both uses of parentheses\u2014as a way to represent a group, as well as a way to express multiplication\u2014are shown.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Simplify [latex]\\left(3+4\\right)^{2}+\\left(8\\right)\\left(4\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q548490\">Show Solution<\/span><\/p>\n<div id=\"q548490\" class=\"hidden-answer\" style=\"display: none\">This problem has parentheses, exponents, multiplication, and addition in it. The first set of parentheses is a grouping symbol. The second set indicates multiplication.<\/p>\n<p>Grouping symbols are handled first. Add numbers in parentheses.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}(3+4)^{2}+(8)(4)\\\\(7)^{2}+(8)(4)\\end{array}[\/latex]<\/p>\n<p>Simplify\u00a0[latex]7^{2}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}7^{2}+(8)(4)\\\\49+(8)(4)\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left;\">Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}49+(8)(4)\\\\49+(32)\\end{array}[\/latex]<\/p>\n<p style=\"text-align: left;\">Add.<\/p>\n<p style=\"text-align: center;\">[latex]49+32=81[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex](3+4)^{2}+(8)(4)=81[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Simplify \u00a0[latex]4\\cdot{\\frac{3[5+{(2 + 3)}^2]}{2}}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q358226\">Show Solution<\/span><\/p>\n<div id=\"q358226\" class=\"hidden-answer\" style=\"display: none\">\n<p>There are brackets and parentheses in this problem. Compute inside the innermost grouping symbols first.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}4\\cdot{\\frac{3[5+{(2 + 3)}^2]}{2}}\\\\\\text{ }\\\\=4\\cdot{\\frac{3[5+{(5)}^2]}{2}}\\end{array}[\/latex]<\/p>\n<p>Then apply the exponent<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}4\\cdot{\\frac{3[5+{(5)}^2]}{2}}\\\\\\text{}\\\\=4\\cdot{\\frac{3[5+25]}{2}}\\\\\\text{ }\\\\=4\\cdot{\\frac{3[30]}{2}}\\end{array}[\/latex]<\/p>\n<p>Then simplify the fraction<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}4\\cdot{\\frac{3[30]}{2}}\\\\\\text{}\\\\=4\\cdot{\\frac{90}{2}}\\\\\\text{ }\\\\=4\\cdot{45}\\\\\\text{ }\\\\=180\\end{array}[\/latex]<\/p>\n<h4 style=\"text-align: left;\">Answer<\/h4>\n<p>[latex]4\\cdot{\\frac{3[5+{(2 + 3)}^2]}{2}}=180[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video, you are shown how to use the order of operations to simplify an expression with grouping symbols, exponents, multiplication, and addition.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-6\" title=\"Simplify an Expression in the Form:  (a+b)^2+c*d\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/EMch2MKCVdA?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Think About It<\/h3>\n<p>These problems are very similar to the examples given above. How are they different and what tools do you need to simplify them?<\/p>\n<p>a) Simplify\u00a0[latex]\\left(1.5+3.5\\right)\u20132\\left(0.5\\cdot6\\right)^{2}[\/latex].\u00a0This problem has parentheses, exponents, multiplication, subtraction, and addition in it, as well as decimals instead of integers.<\/p>\n<p>Use the box below to write down a few thoughts about how you would simplify this expression with decimals and grouping symbols.<\/p>\n<p><textarea aria-label=\"Your Answer\" rows=\"2\"><\/textarea><\/p>\n<p class=\"p1\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q680970\">Show Solution<\/span><\/p>\n<div id=\"q680970\" class=\"hidden-answer\" style=\"display: none\">\nGrouping symbols are handled first. Add numbers in the first set of parentheses.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}(1.5+3.5)\u20132(0.5\\cdot6)^{2}\\\\5\u20132(0.5\\cdot6)^{2}\\end{array}[\/latex]<\/p>\n<p>Multiply numbers in the second set of parentheses.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}5\u20132(0.5\\cdot6)^{2}\\\\5\u20132(3)^{2}\\end{array}[\/latex]<\/p>\n<p>Evaluate exponents.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}5\u20132(3)^{2}\\\\5\u20132\\cdot9\\end{array}[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}5\u20132\\cdot9\\\\5\u201318\\end{array}[\/latex]<\/p>\n<p>Subtract.<\/p>\n<p style=\"text-align: center;\">[latex]5\u201318=\u221213[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex](1.5+3.5)\u20132(0.5\\cdot6)^{2}=\u221213[\/latex]<\/p>\n<\/div>\n<\/div>\n<p class=\"p1\">b) Simplify [latex]{{\\left( \\frac{1}{2} \\right)}^{2}}+{{\\left( \\frac{1}{4} \\right)}^{3}}\\cdot \\,32[\/latex].<\/p>\n<p>Use the box below to write down a few thoughts about how you would simplify this expression with fractions and grouping symbols.<\/p>\n<p><textarea aria-label=\"Your Answer\" rows=\"2\"><\/textarea><\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q680972\">Show Solution<\/span><\/p>\n<div id=\"q680972\" class=\"hidden-answer\" style=\"display: none\">\nThis problem has exponents, multiplication, and addition in it, as well as fractions instead of integers.<\/p>\n<p>According to the order of operations, simplify the terms with the exponents first, then multiply, then add.<\/p>\n<p style=\"text-align: center;\">[latex]\\left(\\frac{1}{2}\\right)^{2}+\\left(\\frac{1}{4}\\right)^{3}\\cdot32[\/latex]<\/p>\n<p>Evaluate: [latex]\\left(\\frac{1}{2}\\right)^{2}=\\frac{1}{2}\\cdot\\frac{1}{2}=\\frac{1}{4}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}+\\left(\\frac{1}{4}\\right)^{3}\\cdot32[\/latex]<\/p>\n<p>Evaluate: [latex]\\left(\\frac{1}{4}\\right)^{3}=\\frac{1}{4}\\cdot\\frac{1}{4}\\cdot\\frac{1}{4}=\\frac{1}{64}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}+\\frac{1}{64}\\cdot32[\/latex]<\/p>\n<p>Multiply.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}+\\frac{32}{64}[\/latex]<\/p>\n<p>Simplify. [latex]\\frac{32}{64}=\\frac{1}{2}[\/latex], so you can add [latex]\\frac{1}{4}+\\frac{1}{2}[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{4}+\\frac{1}{2}=\\frac{3}{4}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]{{\\left( \\frac{1}{2} \\right)}^{2}}+{{\\left( \\frac{1}{4} \\right)}^{3}}\\cdot 32=\\frac{3}{4}[\/latex]<\/p><\/div>\n<\/div>\n<\/div>\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-4509\">\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>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>Order of Operations Staircase. <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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 2: Combining Like Terms. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/b9-7eu29pNM\">https:\/\/youtu.be\/b9-7eu29pNM<\/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>Simplify an Expression in the Form: a-b+c*d. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/yFO_0dlfy-w\">https:\/\/youtu.be\/yFO_0dlfy-w<\/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>Simplify an Expression in the Form: a*1\/b-c\/(1\/d). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/yqp06obmcVc\">https:\/\/youtu.be\/yqp06obmcVc<\/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>Simplify an Expression in the Form: a^n*b^m. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/JjBBgV7G_Qw\">https:\/\/youtu.be\/JjBBgV7G_Qw<\/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>Simplify an Expression in the Form: (a+b)^2+c*d. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/EMch2MKCVdA\">https:\/\/youtu.be\/EMch2MKCVdA<\/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>Unit 9: Real Numbers, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <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><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t 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