{"id":3660,"date":"2020-01-28T04:20:17","date_gmt":"2020-01-28T04:20:17","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3660"},"modified":"2021-02-05T23:50:19","modified_gmt":"2021-02-05T23:50:19","slug":"multiplying-a-polynomial-by-a-monomial","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/multiplying-a-polynomial-by-a-monomial\/","title":{"raw":"Multiplying a Polynomial by a Monomial","rendered":"Multiplying a Polynomial by a Monomial"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Multiply a polynomial by a monomial using the distributive property<\/li>\r\n<\/ul>\r\n<\/div>\r\nPreviously, you learned to use the Distributive Property to simplify expressions such as [latex]2\\left(x - 3\\right)[\/latex]. You multiplied both terms in the parentheses, [latex]x\\text{ and }3[\/latex], by [latex]2[\/latex], to get [latex]2x - 6[\/latex]. With this chapter's new vocabulary, you can say you were multiplying a binomial, [latex]x - 3[\/latex], by a monomial, [latex]2[\/latex]. Multiplying a binomial by a monomial is nothing new for you!\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]3\\left(x+7\\right)[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168468708606\" class=\"unnumbered unstyled\" summary=\"The top line shows 3 times parentheses x plus 7. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\left(x+7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224419\/CNX_BMath_Figure_10_03_001_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]3\\cdot x+3\\cdot 7[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]3x+21[\/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]146197[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]x\\left(x - 8\\right)[\/latex]\r\n[reveal-answer q=\"200462\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"200462\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468567807\" class=\"unnumbered unstyled\" summary=\"The top line shows x times parentheses x minus 8. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x(x-8)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224421\/CNX_BMath_Figure_10_03_044_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x^2-8x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]x^2-8x[\/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]146198[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]10x\\left(4x+y\\right)[\/latex]\r\n[reveal-answer q=\"346464\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"346464\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468433683\" class=\"unnumbered unstyled\" summary=\"The top line shows 10x times parentheses 4x plus y. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]10x(4x+y)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224423\/CNX_BMath_Figure_10_03_045_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]10x\\cdot{4x}+10x\\cdot{y}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]40x^2+10xy[\/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]146201[\/ohm_question]\r\n\r\n<\/div>\r\nMultiplying a monomial by a trinomial works in much the same way.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]-2x\\left(5{x}^{2}+7x - 3\\right)[\/latex]\r\n[reveal-answer q=\"218200\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"218200\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168469497833\" class=\"unnumbered unstyled\" summary=\"The top line shows negative 2x times parentheses 5 x squared plus 7x minus 3. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-2x\\left(5{x}^{2}+7x - 3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224426\/CNX_BMath_Figure_10_03_046_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]-2x\\cdot 5{x}^{2}+\\left(-2x\\right)\\cdot 7x-\\left(-2x\\right)\\cdot 3[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]-10{x}^{3}-14{x}^{2}+6x[\/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]146203[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]4{y}^{3}\\left({y}^{2}-8y+1\\right)[\/latex]\r\n[reveal-answer q=\"648407\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"648407\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168466095135\" class=\"unnumbered unstyled\" summary=\"The top line shows 4 y cubed times parentheses y squared minus 8y plus 1. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4{y}^{3}\\left({y}^{2}-8y+1\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224426\/CNX_BMath_Figure_10_03_047_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]4{y}^{3}\\cdot {y}^{2}-4{y}^{3}\\cdot 8y+4{y}^{3}\\cdot 1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]4{y}^{5}-32{y}^{4}+4{y}^{3}[\/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]146204[\/ohm_question]\r\n\r\n<\/div>\r\nNow we will have the monomial as the second factor.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply: [latex]\\left(x+3\\right)p[\/latex]\r\n[reveal-answer q=\"544089\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"544089\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468557799\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses x plus 3, times p. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(x+3\\right)p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224427\/CNX_BMath_Figure_10_03_048_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]x\\cdot p+3\\cdot p[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]xp+3p[\/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]146206[\/ohm_question]\r\n\r\n<\/div>\r\nIn the following video we show more examples of how to multiply monomials with other polynomials.\r\n\r\nhttps:\/\/youtu.be\/bwTmApTV_8o","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Multiply a polynomial by a monomial using the distributive property<\/li>\n<\/ul>\n<\/div>\n<p>Previously, you learned to use the Distributive Property to simplify expressions such as [latex]2\\left(x - 3\\right)[\/latex]. You multiplied both terms in the parentheses, [latex]x\\text{ and }3[\/latex], by [latex]2[\/latex], to get [latex]2x - 6[\/latex]. With this chapter&#8217;s new vocabulary, you can say you were multiplying a binomial, [latex]x - 3[\/latex], by a monomial, [latex]2[\/latex]. Multiplying a binomial by a monomial is nothing new for you!<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]3\\left(x+7\\right)[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168468708606\" class=\"unnumbered unstyled\" summary=\"The top line shows 3 times parentheses x plus 7. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]3\\left(x+7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224419\/CNX_BMath_Figure_10_03_001_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]3\\cdot x+3\\cdot 7[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]3x+21[\/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=\"ohm146197\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146197&theme=oea&iframe_resize_id=ohm146197&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]x\\left(x - 8\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q200462\">Show Solution<\/span><\/p>\n<div id=\"q200462\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468567807\" class=\"unnumbered unstyled\" summary=\"The top line shows x times parentheses x minus 8. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]x(x-8)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224421\/CNX_BMath_Figure_10_03_044_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]x^2-8x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]x^2-8x[\/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=\"ohm146198\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146198&theme=oea&iframe_resize_id=ohm146198&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]10x\\left(4x+y\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q346464\">Show Solution<\/span><\/p>\n<div id=\"q346464\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468433683\" class=\"unnumbered unstyled\" summary=\"The top line shows 10x times parentheses 4x plus y. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]10x(4x+y)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224423\/CNX_BMath_Figure_10_03_045_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]10x\\cdot{4x}+10x\\cdot{y}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]40x^2+10xy[\/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=\"ohm146201\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146201&theme=oea&iframe_resize_id=ohm146201&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Multiplying a monomial by a trinomial works in much the same way.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]-2x\\left(5{x}^{2}+7x - 3\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q218200\">Show Solution<\/span><\/p>\n<div id=\"q218200\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168469497833\" class=\"unnumbered unstyled\" summary=\"The top line shows negative 2x times parentheses 5 x squared plus 7x minus 3. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]-2x\\left(5{x}^{2}+7x - 3\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224426\/CNX_BMath_Figure_10_03_046_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]-2x\\cdot 5{x}^{2}+\\left(-2x\\right)\\cdot 7x-\\left(-2x\\right)\\cdot 3[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]-10{x}^{3}-14{x}^{2}+6x[\/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=\"ohm146203\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146203&theme=oea&iframe_resize_id=ohm146203&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]4{y}^{3}\\left({y}^{2}-8y+1\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q648407\">Show Solution<\/span><\/p>\n<div id=\"q648407\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168466095135\" class=\"unnumbered unstyled\" summary=\"The top line shows 4 y cubed times parentheses y squared minus 8y plus 1. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]4{y}^{3}\\left({y}^{2}-8y+1\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224426\/CNX_BMath_Figure_10_03_047_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]4{y}^{3}\\cdot {y}^{2}-4{y}^{3}\\cdot 8y+4{y}^{3}\\cdot 1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]4{y}^{5}-32{y}^{4}+4{y}^{3}[\/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=\"ohm146204\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146204&theme=oea&iframe_resize_id=ohm146204&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now we will have the monomial as the second factor.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply: [latex]\\left(x+3\\right)p[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q544089\">Show Solution<\/span><\/p>\n<div id=\"q544089\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468557799\" class=\"unnumbered unstyled\" summary=\"The top line shows parentheses x plus 3, times p. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(x+3\\right)p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224427\/CNX_BMath_Figure_10_03_048_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]x\\cdot p+3\\cdot p[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]xp+3p[\/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=\"ohm146206\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146206&theme=oea&iframe_resize_id=ohm146206&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the following video we show more examples of how to multiply monomials with other polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" 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\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-3660\">\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 146206, 146204, 146203, 146201, 146198, 146197. <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>Ex: Multiplying Using the Distributive Property. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <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><\/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 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