{"id":3662,"date":"2020-01-28T04:21:48","date_gmt":"2020-01-28T04:21:48","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3662"},"modified":"2020-01-28T04:28:02","modified_gmt":"2020-01-28T04:28:02","slug":"multiplying-two-binomials-using-the-distributive-property","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/multiplying-two-binomials-using-the-distributive-property\/","title":{"raw":"Multiplying Two Binomials Using the Distributive Property","rendered":"Multiplying Two Binomials Using the Distributive Property"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the distributive property to multiply two binomials<\/li>\r\n<\/ul>\r\n<\/div>\r\nJust like there are different ways to represent multiplication of numbers, there are several methods that can be used to multiply a binomial times a binomial.\r\n<h3>Using the Distributive Property<\/h3>\r\nWe will start by using the Distributive Property. Look again at the following example.\r\n<table id=\"eip-id1168466233256\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses x plus 3, times p, with red arrows from the p to the x and to the 3. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224428\/CNX_BMath_Figure_10_03_049_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>We distributed the [latex]p[\/latex] to get<\/td>\r\n<td>[latex]x\\color{red}{p}+3\\color{red}{p}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>What if we have [latex]\\left(x+7\\right)[\/latex] instead of [latex]p[\/latex] ?\r\n\r\nThink of the [latex]x+7[\/latex] as the [latex]\\color{red}{p}[\/latex] above.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224430\/CNX_BMath_Figure_10_03_049_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute [latex]\\left(x+7\\right)[\/latex] .<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224432\/CNX_BMath_Figure_10_03_049_img-04.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]{x}^{2}+7x+3x+21[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]{x}^{2}+10x+21[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nNotice that before combining like terms, we had four terms. We multiplied the two terms of the first binomial by the two terms of the second binomial\u2014four multiplications.\r\n\r\nBe careful to distinguish between a sum and a product.\r\n<p style=\"text-align: center\">[latex]\\begin{array}{cccc}\\hfill \\mathbf{\\text{Sum}}\\hfill &amp; &amp; &amp; \\hfill \\mathbf{\\text{Product}}\\hfill \\\\ \\hfill x+x\\hfill &amp; &amp; &amp; \\hfill x\\cdot x\\hfill \\\\ \\hfill 2x\\hfill &amp; &amp; &amp; \\hfill {x}^{2}\\hfill \\\\ \\hfill \\text{combine like terms}\\hfill &amp; &amp; &amp; \\hfill \\text{add exponents of like bases}\\hfill \\end{array}[\/latex]<\/p>\r\n\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(x+6\\right)\\left(x+8\\right)[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468281692\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses x plus 6 times parentheses x plus 8. The next line shows parentheses x plus 6 times red parentheses x plus 8, with red arrows from x plus 8 to x and to 6. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(x+6\\right)\\left(x+8\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224433\/CNX_BMath_Figure_10_03_050_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute [latex]\\left(x+8\\right)[\/latex] .<\/td>\r\n<td>[latex]x\\color{red}{(x+8)}+6\\color{red}{(x+8)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]{x}^{2}+8x+6x+48[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]{x}^{2}+14x+48[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146207[\/ohm_question]\r\n\r\n<\/div>\r\nNow we'll see how to multiply binomials where the variable has a coefficient.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(2x+9\\right)\\left(3x+4\\right)[\/latex]\r\n[reveal-answer q=\"901421\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"901421\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467332174\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses 2x plus 9 times parentheses 3x plus 4. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(2x+9\\right)\\left(3x+4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute. [latex]\\left(3x+4\\right)[\/latex]<\/td>\r\n<td>[latex]2x\\color{red}{(3x+4)}+9\\color{red}{(3x+4)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]6{x}^{2}+8x+27x+36[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]6{x}^{2}+35x+36[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146208[\/ohm_question]\r\n\r\n<\/div>\r\nIn the previous examples, the binomials were sums. When there are differences, we pay special attention to make sure the signs of the product are correct.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(4y+3\\right)\\left(6y - 5\\right)[\/latex]\r\n[reveal-answer q=\"834420\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"834420\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469625351\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses 4y plus 3 times parentheses 6y minus 5. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(4y+3\\right)\\left(6y - 5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]4y\\color{red}{(6y-5)}+3\\color{red}{(6y-5)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]24{y}^{2}-20y+18y - 15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]24{y}^{2}-2y - 15[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146209[\/ohm_question]\r\n\r\n<\/div>\r\nUp to this point, the product of two binomials has been a trinomial. This is not always the case.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(x+2\\right)\\left(x-y\\right)[\/latex]\r\n[reveal-answer q=\"982155\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"982155\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468254725\" class=\"unnumbered unstyled\" summary=\"The top line says parentheses x plus 2 times parentheses x minus y. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex](x+2)(x-y)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]x\\color{red}{(x-y)}+2\\color{red}{(x-y)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute again.<\/td>\r\n<td>[latex]x^2-xy+2x-2y[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>There are no like terms to combine.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146210[\/ohm_question]\r\n\r\n<\/div>\r\nTo see another example of how to visualize multiplying two binomials, watch the following video. We use an area model as well as repeated distribution to multiply two binomials.\r\n\r\nhttps:\/\/youtu.be\/u4Hgl0BrUlo","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the distributive property to multiply two binomials<\/li>\n<\/ul>\n<\/div>\n<p>Just like there are different ways to represent multiplication of numbers, there are several methods that can be used to multiply a binomial times a binomial.<\/p>\n<h3>Using the Distributive Property<\/h3>\n<p>We will start by using the Distributive Property. Look again at the following example.<\/p>\n<table id=\"eip-id1168466233256\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses x plus 3, times p, with red arrows from the p to the x and to the 3. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224428\/CNX_BMath_Figure_10_03_049_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>We distributed the [latex]p[\/latex] to get<\/td>\n<td>[latex]x\\color{red}{p}+3\\color{red}{p}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>What if we have [latex]\\left(x+7\\right)[\/latex] instead of [latex]p[\/latex] ?<\/p>\n<p>Think of the [latex]x+7[\/latex] as the [latex]\\color{red}{p}[\/latex] above.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224430\/CNX_BMath_Figure_10_03_049_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute [latex]\\left(x+7\\right)[\/latex] .<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224432\/CNX_BMath_Figure_10_03_049_img-04.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td>[latex]{x}^{2}+7x+3x+21[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]{x}^{2}+10x+21[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice that before combining like terms, we had four terms. We multiplied the two terms of the first binomial by the two terms of the second binomial\u2014four multiplications.<\/p>\n<p>Be careful to distinguish between a sum and a product.<\/p>\n<p style=\"text-align: center\">[latex]\\begin{array}{cccc}\\hfill \\mathbf{\\text{Sum}}\\hfill & & & \\hfill \\mathbf{\\text{Product}}\\hfill \\\\ \\hfill x+x\\hfill & & & \\hfill x\\cdot x\\hfill \\\\ \\hfill 2x\\hfill & & & \\hfill {x}^{2}\\hfill \\\\ \\hfill \\text{combine like terms}\\hfill & & & \\hfill \\text{add exponents of like bases}\\hfill \\end{array}[\/latex]<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(x+6\\right)\\left(x+8\\right)[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468281692\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses x plus 6 times parentheses x plus 8. The next line shows parentheses x plus 6 times red parentheses x plus 8, with red arrows from x plus 8 to x and to 6. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(x+6\\right)\\left(x+8\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224433\/CNX_BMath_Figure_10_03_050_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute [latex]\\left(x+8\\right)[\/latex] .<\/td>\n<td>[latex]x\\color{red}{(x+8)}+6\\color{red}{(x+8)}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td>[latex]{x}^{2}+8x+6x+48[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]{x}^{2}+14x+48[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146207\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146207&theme=oea&iframe_resize_id=ohm146207&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now we&#8217;ll see how to multiply binomials where the variable has a coefficient.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(2x+9\\right)\\left(3x+4\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q901421\">Show Solution<\/span><\/p>\n<div id=\"q901421\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467332174\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses 2x plus 9 times parentheses 3x plus 4. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(2x+9\\right)\\left(3x+4\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute. [latex]\\left(3x+4\\right)[\/latex]<\/td>\n<td>[latex]2x\\color{red}{(3x+4)}+9\\color{red}{(3x+4)}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td>[latex]6{x}^{2}+8x+27x+36[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]6{x}^{2}+35x+36[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146208\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146208&theme=oea&iframe_resize_id=ohm146208&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the previous examples, the binomials were sums. When there are differences, we pay special attention to make sure the signs of the product are correct.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(4y+3\\right)\\left(6y - 5\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q834420\">Show Solution<\/span><\/p>\n<div id=\"q834420\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469625351\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses 4y plus 3 times parentheses 6y minus 5. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(4y+3\\right)\\left(6y - 5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td>[latex]4y\\color{red}{(6y-5)}+3\\color{red}{(6y-5)}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td>[latex]24{y}^{2}-20y+18y - 15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]24{y}^{2}-2y - 15[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146209\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146209&theme=oea&iframe_resize_id=ohm146209&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Up to this point, the product of two binomials has been a trinomial. This is not always the case.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(x+2\\right)\\left(x-y\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q982155\">Show Solution<\/span><\/p>\n<div id=\"q982155\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468254725\" class=\"unnumbered unstyled\" summary=\"The top line says parentheses x plus 2 times parentheses x minus y. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex](x+2)(x-y)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td>[latex]x\\color{red}{(x-y)}+2\\color{red}{(x-y)}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute again.<\/td>\n<td>[latex]x^2-xy+2x-2y[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>There are no like terms to combine.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146210\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146210&theme=oea&iframe_resize_id=ohm146210&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>To see another example of how to visualize multiplying two binomials, watch the following video. We use an area model as well as repeated distribution to multiply two binomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Multiply Binomials Using An Area Model and Using Repeated Distribution\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/u4Hgl0BrUlo?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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-3662\">\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>Question ID 146210, 146209,  146208, 146207. <strong>Authored 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>Multiply Binomials Using An Area Model and Using Repeated Distribution. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <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><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <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\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/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":25777,"menu_order":19,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146210, 146209,  146208, 146207\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Multiply Binomials Using An Area Model and Using Repeated Distribution\",\"author\":\"James Sousa 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