{"id":10840,"date":"2017-06-05T21:25:47","date_gmt":"2017-06-05T21:25:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10840"},"modified":"2017-09-24T00:35:33","modified_gmt":"2017-09-24T00:35:33","slug":"multiplying-a-trinomial-by-a-binomial","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/multiplying-a-trinomial-by-a-binomial\/","title":{"raw":"Multiplying a Trinomial By a Binomial","rendered":"Multiplying a Trinomial By a Binomial"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Multiply a trinomial by a binomial<\/li>\r\n<\/ul>\r\n<\/div>\r\nWe have multiplied monomials by monomials, monomials by polynomials, and binomials by binomials. Now we're ready to multiply a trinomial by a binomial. Remember, the FOIL method will not work in this case, but we can use either the Distributive Property or the Vertical Method. We first look at an example using the Distributive Property.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply using the Distributive Property: [latex]\\left(x+3\\right)\\left(2{x}^{2}-5x+8\\right)[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168467363028\" class=\"unnumbered unstyled\" summary=\"A vertical multiplication problem is shown. 2 x squared minus 5x plus 8 times x plus 3 is written, with a line beneath it. 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\/24224530\/CNX_BMath_Figure_10_03_061_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Distribute.<\/td>\r\n<td>[latex]x\\color{red}{(2x^2-5x+8)}+3\\color{red}{(2x^2-5x+8)}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]2{x}^{3}-5{x}^{2}+8x+6{x}^{2}-15x+24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Combine like terms.<\/td>\r\n<td>[latex]2{x}^{3}+{x}^{2}-7x+24[\/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]146217[\/ohm_question]\r\n\r\n<\/div>\r\nNow let's do this same multiplication using the Vertical Method.\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nMultiply using the Vertical Method: [latex]\\left(x+3\\right)\\left(2{x}^{2}-5x+8\\right)[\/latex]\r\n[reveal-answer q=\"80068\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"80068\"]\r\n\r\nSolution\r\nIt is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.\r\n<table id=\"eip-id1168469786876\" class=\"unnumbered unstyled\" summary=\"A vertical multiplication problem is shown. 2 x squared minus 5x plus 8 times x plus 3 is written, with a line beneath it. 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\/24224533\/CNX_BMath_Figure_10_03_062_img-01.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply [latex]\\left(2{x}^{2}-5x+8\\right)[\/latex] by [latex]3[\/latex].<\/td>\r\n<td>[latex]6x^2-15x+24[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply [latex]\\left(2{x}^{2}-5x+8\\right)[\/latex] by [latex]x[\/latex] .<\/td>\r\n<td>[latex]2x^3-5x^2+8x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add like terms.<\/td>\r\n<td>[latex]2x^3+x^2-7x+24[\/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]146218[\/ohm_question]\r\n\r\n<\/div>\r\nWatch the following video to see more examples of multiplying polynomials.\r\n\r\nhttps:\/\/youtu.be\/bBKbldmlbqI","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Multiply a trinomial by a binomial<\/li>\n<\/ul>\n<\/div>\n<p>We have multiplied monomials by monomials, monomials by polynomials, and binomials by binomials. Now we&#8217;re ready to multiply a trinomial by a binomial. Remember, the FOIL method will not work in this case, but we can use either the Distributive Property or the Vertical Method. We first look at an example using the Distributive Property.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply using the Distributive Property: [latex]\\left(x+3\\right)\\left(2{x}^{2}-5x+8\\right)[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467363028\" class=\"unnumbered unstyled\" summary=\"A vertical multiplication problem is shown. 2 x squared minus 5x plus 8 times x plus 3 is written, with a line beneath it. 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\/24224530\/CNX_BMath_Figure_10_03_061_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Distribute.<\/td>\n<td>[latex]x\\color{red}{(2x^2-5x+8)}+3\\color{red}{(2x^2-5x+8)}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]2{x}^{3}-5{x}^{2}+8x+6{x}^{2}-15x+24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Combine like terms.<\/td>\n<td>[latex]2{x}^{3}+{x}^{2}-7x+24[\/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=\"ohm146217\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146217&theme=oea&iframe_resize_id=ohm146217&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Now let&#8217;s do this same multiplication using the Vertical Method.<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Multiply using the Vertical Method: [latex]\\left(x+3\\right)\\left(2{x}^{2}-5x+8\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q80068\">Show Solution<\/span><\/p>\n<div id=\"q80068\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nIt is easier to put the polynomial with fewer terms on the bottom because we get fewer partial products this way.<\/p>\n<table id=\"eip-id1168469786876\" class=\"unnumbered unstyled\" summary=\"A vertical multiplication problem is shown. 2 x squared minus 5x plus 8 times x plus 3 is written, with a line beneath it. 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\/24224533\/CNX_BMath_Figure_10_03_062_img-01.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Multiply [latex]\\left(2{x}^{2}-5x+8\\right)[\/latex] by [latex]3[\/latex].<\/td>\n<td>[latex]6x^2-15x+24[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply [latex]\\left(2{x}^{2}-5x+8\\right)[\/latex] by [latex]x[\/latex] .<\/td>\n<td>[latex]2x^3-5x^2+8x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add like terms.<\/td>\n<td>[latex]2x^3+x^2-7x+24[\/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=\"ohm146218\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146218&theme=oea&iframe_resize_id=ohm146218&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Watch the following video to see more examples of multiplying polynomials.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"(New Version Available) Polynomial Multiplication Involving Binomials and Trinomials\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/bBKbldmlbqI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\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-10840\">\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 146218, 146217. <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: Polynomial Multiplication Involving Binomials and Trinomials. <strong>Authored by<\/strong>: Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/bBKbldmlbqI\">https:\/\/youtu.be\/bBKbldmlbqI<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div 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":21046,"menu_order":16,"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 146218, 146217\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Polynomial Multiplication Involving Binomials and Trinomials\",\"author\":\"Lumen 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