{"id":17874,"date":"2020-04-11T23:33:56","date_gmt":"2020-04-11T23:33:56","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/wm-developmentalemporium\/?post_type=chapter&p=17874"},"modified":"2020-10-22T09:33:32","modified_gmt":"2020-10-22T09:33:32","slug":"summary-special-cases","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/chapter\/summary-special-cases\/","title":{"raw":"13.3.d - Summary: Factoring Special Cases","rendered":"13.3.d – Summary: Factoring Special Cases"},"content":{"raw":"

Key Concepts<\/h2>\r\nPerfect Square Trinomials\u00a0\u00a0<\/strong>A perfect square trinomial can be written as the square of a binomial:\r\n
[latex]{a}^{2}+2ab+{b}^{2}={\\left(a+b\\right)}^{2}[\/latex]<\/div>\r\n
[latex]{a}^{2}-2ab+{b}^{2}={\\left(a-b\\right)}^{2}[\/latex]<\/div>\r\n
\r\n\r\nHow to factor a perfect square trinomial\r\n<\/strong>\r\n
    \r\n \t
  1. Confirm that the first and last term are perfect squares.<\/li>\r\n \t
  2. Confirm that the middle term is twice the product of [latex]ab[\/latex].<\/li>\r\n \t
  3. Write the factored form as [latex]{\\left(a+b\\right)}^{2}[\/latex] or [latex]{\\left(a-b\\right)}^{2}[\/latex].<\/li>\r\n<\/ol>\r\nDifferences of Squares\u00a0\u00a0<\/strong>A difference of squares can be rewritten as two factors containing the same terms but opposite signs.\r\n
    [latex]{a}^{2}-{b}^{2}=\\left(a+b\\right)\\left(a-b\\right)[\/latex]<\/div>\r\n
    \r\n\r\nThe Sum of Cubes<\/strong>\u00a0 A binomial in the form [latex]a^{3}+b^{3}[\/latex] can be factored as [latex]\\left(a+b\\right)\\left(a^{2}\u2013ab+b^{2}\\right)[\/latex].\r\n\r\nThe Difference of Cubes\u00a0\u00a0<\/strong>A binomial in the form [latex]a^{3}\u2013b^{3}[\/latex] can be factored as [latex]\\left(a-b\\right)\\left(a^{2}+ab+b^{2}\\right)[\/latex].\r\n\r\n<\/div>\r\n<\/div>","rendered":"

    Key Concepts<\/h2>\n

    Perfect Square Trinomials\u00a0\u00a0<\/strong>A perfect square trinomial can be written as the square of a binomial:<\/p>\n

    [latex]{a}^{2}+2ab+{b}^{2}={\\left(a+b\\right)}^{2}[\/latex]<\/div>\n
    [latex]{a}^{2}-2ab+{b}^{2}={\\left(a-b\\right)}^{2}[\/latex]<\/div>\n
    \n

    How to factor a perfect square trinomial
    \n<\/strong><\/p>\n

      \n
    1. Confirm that the first and last term are perfect squares.<\/li>\n
    2. Confirm that the middle term is twice the product of [latex]ab[\/latex].<\/li>\n
    3. Write the factored form as [latex]{\\left(a+b\\right)}^{2}[\/latex] or [latex]{\\left(a-b\\right)}^{2}[\/latex].<\/li>\n<\/ol>\n

      Differences of Squares\u00a0\u00a0<\/strong>A difference of squares can be rewritten as two factors containing the same terms but opposite signs.<\/p>\n

      [latex]{a}^{2}-{b}^{2}=\\left(a+b\\right)\\left(a-b\\right)[\/latex]<\/div>\n
      \n

      The Sum of Cubes<\/strong>\u00a0 A binomial in the form [latex]a^{3}+b^{3}[\/latex] can be factored as [latex]\\left(a+b\\right)\\left(a^{2}\u2013ab+b^{2}\\right)[\/latex].<\/p>\n

      The Difference of Cubes\u00a0\u00a0<\/strong>A binomial in the form [latex]a^{3}\u2013b^{3}[\/latex] can be factored as [latex]\\left(a-b\\right)\\left(a^{2}+ab+b^{2}\\right)[\/latex].<\/p>\n<\/div>\n<\/div>\n","protected":false},"author":253111,"menu_order":17,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"933680a871454fc6912430bf6e5dd586","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-17874","chapter","type-chapter","status-publish","hentry"],"part":16188,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17874","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/users\/253111"}],"version-history":[{"count":6,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17874\/revisions"}],"predecessor-version":[{"id":20423,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17874\/revisions\/20423"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/parts\/16188"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapters\/17874\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/media?parent=17874"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/pressbooks\/v2\/chapter-type?post=17874"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/contributor?post=17874"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-rockland-developmentalemporium\/wp-json\/wp\/v2\/license?post=17874"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}