{"id":10816,"date":"2017-06-05T21:00:33","date_gmt":"2017-06-05T21:00:33","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10816"},"modified":"2020-07-02T02:47:53","modified_gmt":"2020-07-02T02:47:53","slug":"summary-adding-and-subtracting-polynomials","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/summary-adding-and-subtracting-polynomials\/","title":{"raw":"Summary: Performing Operations on Polynomials","rendered":"Summary: Performing Operations on Polynomials"},"content":{"raw":"<dl id=\"fs-id1166478400952\" class=\"definition\">\r\n \t<dd id=\"fs-id1166478400957\"><span style=\"color: #077fab; font-size: 1.15em; font-weight: 600;\">Key Concepts<\/span><\/dd>\r\n<\/dl>\r\n<ul id=\"eip-373\">\r\n \t<li><strong>Given multiple polynomials, how to add or subtract them to simplify the expressions\r\n<\/strong>\r\n<ol>\r\n \t<li>Combine like terms.<\/li>\r\n \t<li>Simplify and write in standard form.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li><strong>Use the FOIL method for multiplying two binomials.<\/strong>\r\n<table id=\"eip-208\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>Step 1. Multiply the <strong>First<\/strong> terms.<\/td>\r\n<td rowspan=\"6\">&nbsp;\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224442\/CNX_BMath_Figure_10_03_025_img.png\" alt=\".\" \/><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 2. Multiply the <strong>Outer<\/strong> terms.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 3. Multiply the <strong>Inner<\/strong> terms.<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 4. Multiply the <strong>Last<\/strong> terms.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Step 5. Combine like terms, when possible.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n \t<li><strong>Multiplying Two Binomials:<\/strong> To multiply binomials, use the:\r\n<ul id=\"eip-id1170325412264\">\r\n \t<li>Distributive Property<\/li>\r\n \t<li>FOIL Method<\/li>\r\n \t<li>Vertical Method<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li><strong>Multiplying a Trinomial by a Binomial:<\/strong> To multiply a trinomial by a binomial, use the:\r\n<ul id=\"eip-id1170324224435\">\r\n \t<li>Distributive Property<\/li>\r\n \t<li>Vertical Method<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h2>Contribute!<\/h2><div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div><a href=\"https:\/\/docs.google.com\/document\/d\/1Ij6iPG2Ueg3tUC7nEXr-g_dRLohHAU4iup0PyR1tzsI\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a>","rendered":"<dl id=\"fs-id1166478400952\" class=\"definition\">\n<dd id=\"fs-id1166478400957\"><span style=\"color: #077fab; font-size: 1.15em; font-weight: 600;\">Key Concepts<\/span><\/dd>\n<\/dl>\n<ul id=\"eip-373\">\n<li><strong>Given multiple polynomials, how to add or subtract them to simplify the expressions<br \/>\n<\/strong><\/p>\n<ol>\n<li>Combine like terms.<\/li>\n<li>Simplify and write in standard form.<\/li>\n<\/ol>\n<\/li>\n<li><strong>Use the FOIL method for multiplying two binomials.<\/strong><br \/>\n<table id=\"eip-208\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>Step 1. Multiply the <strong>First<\/strong> terms.<\/td>\n<td rowspan=\"6\">&nbsp;<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24224442\/CNX_BMath_Figure_10_03_025_img.png\" alt=\".\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 2. Multiply the <strong>Outer<\/strong> terms.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 3. Multiply the <strong>Inner<\/strong> terms.<\/td>\n<\/tr>\n<tr>\n<td>Step 4. Multiply the <strong>Last<\/strong> terms.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 5. Combine like terms, when possible.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li><strong>Multiplying Two Binomials:<\/strong> To multiply binomials, use the:\n<ul id=\"eip-id1170325412264\">\n<li>Distributive Property<\/li>\n<li>FOIL Method<\/li>\n<li>Vertical Method<\/li>\n<\/ul>\n<\/li>\n<li><strong>Multiplying a Trinomial by a Binomial:<\/strong> To multiply a trinomial by a binomial, use the:\n<ul id=\"eip-id1170324224435\">\n<li>Distributive Property<\/li>\n<li>Vertical Method<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a href=\"https:\/\/docs.google.com\/document\/d\/1Ij6iPG2Ueg3tUC7nEXr-g_dRLohHAU4iup0PyR1tzsI\" target=\"_blank\" style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\">Improve this page<\/a><a style=\"margin-left: 16px;\" target=\"_blank\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\">Learn More<\/a><\/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-10816\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><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":17533,"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\"}]","CANDELA_OUTCOMES_GUID":"900491ffb15747d7abbbe31f06329d3c","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-10816","chapter","type-chapter","status-publish","hentry"],"part":8336,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/10816","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":11,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/10816\/revisions"}],"predecessor-version":[{"id":19023,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/10816\/revisions\/19023"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/parts\/8336"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapters\/10816\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/media?parent=10816"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/pressbooks\/v2\/chapter-type?post=10816"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/contributor?post=10816"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/wp-json\/wp\/v2\/license?post=10816"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}