{"id":3650,"date":"2020-01-28T02:02:36","date_gmt":"2020-01-28T02:02:36","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3650"},"modified":"2020-01-28T02:06:18","modified_gmt":"2020-01-28T02:06:18","slug":"adding-and-subtracting-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/mathforliberalartscorequisite\/chapter\/adding-and-subtracting-polynomials\/","title":{"raw":"Adding and Subtracting Polynomials","rendered":"Adding and Subtracting Polynomials"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Add polynomials<\/li>\r\n \t<li>Subtract polynomials<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn a previous lesson, you learned how to simplify expressions by combining like terms. Adding and subtracting monomials is the same as combining like terms. Like terms must have the same variable with the same exponent. Recall that when combining like terms only the coefficients are combined, never the exponents.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nAdd: [latex]17{x}^{2}+6{x}^{2}[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168469711517\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]17{x}^{2}+6{x}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]23{x}^{2}[\/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]146075[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSubtract: [latex]11n-\\left(-8n\\right)[\/latex]\r\n[reveal-answer q=\"915884\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"915884\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468510729\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]11n-\\left(-8n\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]19n[\/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]146315[\/ohm_question]\r\n\r\n[ohm_question]146077[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify: [latex]{a}^{2}+4{b}^{2}-7{a}^{2}[\/latex]\r\n[reveal-answer q=\"15776\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"15776\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468675660\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{a}^{2}+4{b}^{2}-7{a}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]-6{a}^{{}^{2}}+4{b}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nRemember, [latex]-6{a}^{2}[\/latex] and [latex]4{b}^{2}[\/latex] are not like terms. The variables are not the same.\r\n\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]146078[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video for more examples of how to multiply polynomials.\r\n\r\nhttps:\/\/youtu.be\/KYZR7g7QcF4\r\n<h3>Add and Subtract Polynomials<\/h3>\r\nAdding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms\u2014those with the same variables with the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nFind the sum: [latex]\\left(4{x}^{2}-5x+1\\right)+\\left(3{x}^{2}-8x - 9\\right)[\/latex].\r\n[reveal-answer q=\"337728\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"337728\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468393629\" class=\"unnumbered unstyled\" summary=\"The top row shows parentheses 4 x squared minus 5x plus 1 plus parentheses 3 x squared minus 8x minus 9. The next row says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(4{x}^{2}-5x+1\\right)+\\left(3{x}^{2}-8x - 9\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Identify like terms.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224334\/CNX_BMath_Figure_10_01_003-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange to get the like terms together.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224335\/CNX_BMath_Figure_10_01_003_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]7x^2-13x-8[\/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]146084[\/ohm_question]\r\n\r\n<\/div>\r\nParentheses are grouping symbols. When we add polynomials as we did in the last example, we can rewrite the expression without parentheses and then combine like terms. But when we subtract polynomials, we must be very careful with the signs.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nFind the difference: [latex]\\left(7{u}^{2}-5u+3\\right)-\\left(4{u}^{2}-2\\right)[\/latex].\r\n[reveal-answer q=\"295369\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"295369\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468667646\" class=\"unnumbered unstyled\" summary=\"The top row shows parentheses 7 u squared minus 5u plus 3 minus parentheses 4 u squared minus 2. The next line says, \">\r\n<tbody>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]\\left(7{u}^{2}-5u+3\\right)-\\left(4{u}^{2}-2\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute and identify like terms.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224338\/CNX_BMath_Figure_10_01_004_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange the terms.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224339\/CNX_BMath_Figure_10_01_004_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]3{u}^{2}-5u+5[\/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]146079[\/ohm_question]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\nSubtract [latex]\\left({m}^{2}-3m+8\\right)[\/latex] from [latex]\\left(9{m}^{2}-7m+4\\right)[\/latex].\r\n[reveal-answer q=\"661227\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"661227\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168467283477\" class=\"unnumbered unstyled\" summary=\"The top line says, \">\r\n<tbody>\r\n<tr>\r\n<td>\u00a0Subtract [latex]\\left({m}^{2}-3m+8\\right)[\/latex] from [latex]\\left(9{m}^{2}-7m+4\\right)[\/latex].<\/td>\r\n<td>[latex](9{m}^{2}-7m+4)-({m}^{2}-3m+8)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute and identify like terms.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224343\/CNX_BMath_Figure_10_01_005_img-02.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Rearrange the terms.<\/td>\r\n<td><img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224345\/CNX_BMath_Figure_10_01_005_img-03.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]8m^2-4m-4[\/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\u00a0IT<\/h3>\r\n[ohm_question]146085[\/ohm_question]\r\n\r\n<\/div>\r\nIn the next video we show more examples of adding and subtracting polynomials.\r\n\r\nhttps:\/\/youtu.be\/jiq3toC7wGM","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Add polynomials<\/li>\n<li>Subtract polynomials<\/li>\n<\/ul>\n<\/div>\n<p>In a previous lesson, you learned how to simplify expressions by combining like terms. Adding and subtracting monomials is the same as combining like terms. Like terms must have the same variable with the same exponent. Recall that when combining like terms only the coefficients are combined, never the exponents.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Add: [latex]17{x}^{2}+6{x}^{2}[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168469711517\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]17{x}^{2}+6{x}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]23{x}^{2}[\/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=\"ohm146075\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146075&theme=oea&iframe_resize_id=ohm146075&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>Subtract: [latex]11n-\\left(-8n\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q915884\">Show Solution<\/span><\/p>\n<div id=\"q915884\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468510729\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]11n-\\left(-8n\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]19n[\/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=\"ohm146315\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146315&theme=oea&iframe_resize_id=ohm146315&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146077\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146077&theme=oea&iframe_resize_id=ohm146077&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>Simplify: [latex]{a}^{2}+4{b}^{2}-7{a}^{2}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q15776\">Show Solution<\/span><\/p>\n<div id=\"q15776\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468675660\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]{a}^{2}+4{b}^{2}-7{a}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]-6{a}^{{}^{2}}+4{b}^{2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Remember, [latex]-6{a}^{2}[\/latex] and [latex]4{b}^{2}[\/latex] are not like terms. The variables are not the same.<\/p>\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=\"ohm146078\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146078&theme=oea&iframe_resize_id=ohm146078&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video for more examples of how to multiply polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex:  Adding Polynomials\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/KYZR7g7QcF4?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<h3>Add and Subtract Polynomials<\/h3>\n<p>Adding and subtracting polynomials can be thought of as just adding and subtracting like terms. Look for like terms\u2014those with the same variables with the same exponent. The Commutative Property allows us to rearrange the terms to put like terms together. It may also be helpful to underline, circle, or box like terms.<\/p>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Find the sum: [latex]\\left(4{x}^{2}-5x+1\\right)+\\left(3{x}^{2}-8x - 9\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q337728\">Show Solution<\/span><\/p>\n<div id=\"q337728\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468393629\" class=\"unnumbered unstyled\" summary=\"The top row shows parentheses 4 x squared minus 5x plus 1 plus parentheses 3 x squared minus 8x minus 9. The next row says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(4{x}^{2}-5x+1\\right)+\\left(3{x}^{2}-8x - 9\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Identify like terms.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224334\/CNX_BMath_Figure_10_01_003-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rearrange to get the like terms together.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224335\/CNX_BMath_Figure_10_01_003_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]7x^2-13x-8[\/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=\"ohm146084\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146084&theme=oea&iframe_resize_id=ohm146084&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Parentheses are grouping symbols. When we add polynomials as we did in the last example, we can rewrite the expression without parentheses and then combine like terms. But when we subtract polynomials, we must be very careful with the signs.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Find the difference: [latex]\\left(7{u}^{2}-5u+3\\right)-\\left(4{u}^{2}-2\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q295369\">Show Solution<\/span><\/p>\n<div id=\"q295369\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468667646\" class=\"unnumbered unstyled\" summary=\"The top row shows parentheses 7 u squared minus 5u plus 3 minus parentheses 4 u squared minus 2. The next line says,\">\n<tbody>\n<tr>\n<td><\/td>\n<td>[latex]\\left(7{u}^{2}-5u+3\\right)-\\left(4{u}^{2}-2\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute and identify like terms.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224338\/CNX_BMath_Figure_10_01_004_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the terms.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224339\/CNX_BMath_Figure_10_01_004_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]3{u}^{2}-5u+5[\/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=\"ohm146079\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146079&theme=oea&iframe_resize_id=ohm146079&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<p>Subtract [latex]\\left({m}^{2}-3m+8\\right)[\/latex] from [latex]\\left(9{m}^{2}-7m+4\\right)[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q661227\">Show Solution<\/span><\/p>\n<div id=\"q661227\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168467283477\" class=\"unnumbered unstyled\" summary=\"The top line says,\">\n<tbody>\n<tr>\n<td>\u00a0Subtract [latex]\\left({m}^{2}-3m+8\\right)[\/latex] from [latex]\\left(9{m}^{2}-7m+4\\right)[\/latex].<\/td>\n<td>[latex](9{m}^{2}-7m+4)-({m}^{2}-3m+8)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Distribute and identify like terms.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224343\/CNX_BMath_Figure_10_01_005_img-02.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Rearrange the terms.<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224345\/CNX_BMath_Figure_10_01_005_img-03.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]8m^2-4m-4[\/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\u00a0IT<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146085\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146085&theme=oea&iframe_resize_id=ohm146085&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>In the next video we show more examples of adding and subtracting polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" 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\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-3650\">\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 146085, 146084, 146078, 146070, 146073. <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: Adding Polynomials. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/KYZR7g7QcF4\">https:\/\/youtu.be\/KYZR7g7QcF4<\/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><\/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":12,"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 146085, 146084, 146078, 146070, 146073\",\"author\":\"Lumen 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