{"id":1899,"date":"2021-12-02T19:39:53","date_gmt":"2021-12-03T00:39:53","guid":{"rendered":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-3\/"},"modified":"2023-09-01T14:15:39","modified_gmt":"2023-09-01T18:15:39","slug":"answer-key-7-3","status":"publish","type":"back-matter","link":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/back-matter\/answer-key-7-3\/","title":{"raw":"Answer Key 7.3","rendered":"Answer Key 7.3"},"content":{"raw":"
    \r\n \t
  1. [latex]9\\times 8 = 72[\/latex]\r\n[latex]9+8=17[\/latex]\r\n[latex]p^2+9p+8p+72[\/latex]\r\n[latex]p(p+9)+8(p+9)[\/latex]\r\n[latex](p+9)(p+8)[\/latex]<\/li>\r\n \t
  2. [latex]9\\times -8=-72[\/latex]\r\n[latex]9+-8=1[\/latex]\r\n[latex]x^2+9x-8x-72[\/latex]\r\n[latex]x(x+9)-8(x+9)[\/latex]\r\n[latex](x+9)(x-8)[\/latex]<\/li>\r\n \t
  3. [latex]-8\\times -1 = 8[\/latex]\r\n[latex]-8+-1=-9[\/latex]\r\n[latex]n^2-n-8n+8[\/latex]\r\n[latex]n(n-1)-8(n-1)[\/latex]\r\n[latex](n-1)(n-8)[\/latex]<\/li>\r\n \t
  4. [latex]6\\times -5 = -30[\/latex]\r\n[latex]6+-5=1[\/latex]\r\n[latex]x^2+6x-5x-30[\/latex]\r\n[latex]x(x+6)-5(x+6)[\/latex]\r\n[latex](x+6)(x-5)[\/latex]<\/li>\r\n \t
  5. [latex]-10\\times 1 = -10[\/latex]\r\n[latex]-10+1=-9[\/latex]\r\n[latex]x^2-10x+x-10[\/latex]\r\n[latex]x(x-10)+1(x-10)[\/latex]\r\n[latex](x-10)(x+1)[\/latex]<\/li>\r\n \t
  6. [latex]8\\times 5 = 40[\/latex]\r\n[latex]8+5=13[\/latex]\r\n[latex]x^2+8x+5x+40[\/latex]\r\n[latex]x(x+8)+5(x+8)[\/latex]\r\n[latex](x+8)(x+5)[\/latex]<\/li>\r\n \t
  7. [latex]4\\times 8 =32[\/latex]\r\n[latex]4+8=12[\/latex]\r\n[latex]b^2+4b+8b+32[\/latex]\r\n[latex]b(b+4)+8(b+4)[\/latex]\r\n[latex](b+4)(b+8)[\/latex]<\/li>\r\n \t
  8. [latex]-7\\times -10=70[\/latex]\r\n[latex]-7+-10=-17[\/latex]\r\n[latex]b^2-7b-10b+70[\/latex]\r\n[latex]b(b-7)-10(b-7)[\/latex]\r\n[latex](b-7)(b-10)[\/latex]<\/li>\r\n \t
  9. [latex]-3\\times -5=15[\/latex]\r\n[latex]-3+-5=-8[\/latex]\r\n[latex]u^2-3uv-5uv+15v^2[\/latex]\r\n[latex]u(u-3v)-5v(u-3v)[\/latex]\r\n[latex](u-3v)(u-5v)[\/latex]<\/li>\r\n \t
  10. [latex]-8\\times 5 =-40[\/latex]\r\n[latex]-8+5=-3[\/latex]\r\n[latex]m^2-8mn+5mn-40n^2[\/latex]\r\n[latex]m(m-8n)+5n(m-8n)[\/latex]\r\n[latex](m-8n)(m+5n)[\/latex]<\/li>\r\n \t
  11. [latex]4\\times -2=-8[\/latex]\r\n[latex]4+-2=2[\/latex]\r\n[latex]m^2+4mn-2mn-8n^2[\/latex]\r\n[latex]m(m+4n)-2n(m+4n)[\/latex]\r\n[latex](m+4n)(m-2n)[\/latex]<\/li>\r\n \t
  12. [latex]8\\times 2=16[\/latex]\r\n[latex]8+2=10[\/latex]\r\n[latex]x^2+8xy+2xy+16y^2[\/latex]\r\n[latex]x(x+8y)+2y(x+8y)[\/latex]\r\n[latex](x+8y)(x+2y)[\/latex]<\/li>\r\n \t
  13. [latex]-9\\times -2=18[\/latex]\r\n[latex]-9+-2=-11[\/latex]\r\n[latex]x^2-9xy-2xy+18y^2[\/latex]\r\n[latex]x(x-9y)-2y(x-9y)[\/latex]\r\n[latex](x-9y)(x-2y)[\/latex]<\/li>\r\n \t
  14. [latex]-2\\times -7=14[\/latex]\r\n[latex]-2+-7=-9[\/latex]\r\n[latex]u^2-2uv-7uv+14v^2[\/latex]\r\n[latex]u(u-2v)-7v(u-2v)[\/latex]\r\n[latex](u-2v)(u-7v)[\/latex]<\/li>\r\n \t
  15. [latex]4\\times -3=-12[\/latex]\r\n[latex]4+-3=1[\/latex]\r\n[latex]x^2+4xy-3xy-12y^2[\/latex]\r\n[latex]x(x+4y)-3y(x+4y)[\/latex]\r\n[latex](x+4y)(x-3y)[\/latex]<\/li>\r\n \t
  16. [latex]5\\times 9=45[\/latex]\r\n[latex]5+9=14[\/latex]\r\n[latex]x^2+5xy+9xy+45y^2[\/latex]\r\n[latex]x(x+5y)+9y(x+5y)[\/latex]\r\n[latex](x+5y)(x+9y)[\/latex]<\/li>\r\n<\/ol>","rendered":"
      \n
    1. [latex]9\\times 8 = 72[\/latex]
      \n[latex]9+8=17[\/latex]
      \n[latex]p^2+9p+8p+72[\/latex]
      \n[latex]p(p+9)+8(p+9)[\/latex]
      \n[latex](p+9)(p+8)[\/latex]<\/li>\n
    2. [latex]9\\times -8=-72[\/latex]
      \n[latex]9+-8=1[\/latex]
      \n[latex]x^2+9x-8x-72[\/latex]
      \n[latex]x(x+9)-8(x+9)[\/latex]
      \n[latex](x+9)(x-8)[\/latex]<\/li>\n
    3. [latex]-8\\times -1 = 8[\/latex]
      \n[latex]-8+-1=-9[\/latex]
      \n[latex]n^2-n-8n+8[\/latex]
      \n[latex]n(n-1)-8(n-1)[\/latex]
      \n[latex](n-1)(n-8)[\/latex]<\/li>\n
    4. [latex]6\\times -5 = -30[\/latex]
      \n[latex]6+-5=1[\/latex]
      \n[latex]x^2+6x-5x-30[\/latex]
      \n[latex]x(x+6)-5(x+6)[\/latex]
      \n[latex](x+6)(x-5)[\/latex]<\/li>\n
    5. [latex]-10\\times 1 = -10[\/latex]
      \n[latex]-10+1=-9[\/latex]
      \n[latex]x^2-10x+x-10[\/latex]
      \n[latex]x(x-10)+1(x-10)[\/latex]
      \n[latex](x-10)(x+1)[\/latex]<\/li>\n
    6. [latex]8\\times 5 = 40[\/latex]
      \n[latex]8+5=13[\/latex]
      \n[latex]x^2+8x+5x+40[\/latex]
      \n[latex]x(x+8)+5(x+8)[\/latex]
      \n[latex](x+8)(x+5)[\/latex]<\/li>\n
    7. [latex]4\\times 8 =32[\/latex]
      \n[latex]4+8=12[\/latex]
      \n[latex]b^2+4b+8b+32[\/latex]
      \n[latex]b(b+4)+8(b+4)[\/latex]
      \n[latex](b+4)(b+8)[\/latex]<\/li>\n
    8. [latex]-7\\times -10=70[\/latex]
      \n[latex]-7+-10=-17[\/latex]
      \n[latex]b^2-7b-10b+70[\/latex]
      \n[latex]b(b-7)-10(b-7)[\/latex]
      \n[latex](b-7)(b-10)[\/latex]<\/li>\n
    9. [latex]-3\\times -5=15[\/latex]
      \n[latex]-3+-5=-8[\/latex]
      \n[latex]u^2-3uv-5uv+15v^2[\/latex]
      \n[latex]u(u-3v)-5v(u-3v)[\/latex]
      \n[latex](u-3v)(u-5v)[\/latex]<\/li>\n
    10. [latex]-8\\times 5 =-40[\/latex]
      \n[latex]-8+5=-3[\/latex]
      \n[latex]m^2-8mn+5mn-40n^2[\/latex]
      \n[latex]m(m-8n)+5n(m-8n)[\/latex]
      \n[latex](m-8n)(m+5n)[\/latex]<\/li>\n
    11. [latex]4\\times -2=-8[\/latex]
      \n[latex]4+-2=2[\/latex]
      \n[latex]m^2+4mn-2mn-8n^2[\/latex]
      \n[latex]m(m+4n)-2n(m+4n)[\/latex]
      \n[latex](m+4n)(m-2n)[\/latex]<\/li>\n
    12. [latex]8\\times 2=16[\/latex]
      \n[latex]8+2=10[\/latex]
      \n[latex]x^2+8xy+2xy+16y^2[\/latex]
      \n[latex]x(x+8y)+2y(x+8y)[\/latex]
      \n[latex](x+8y)(x+2y)[\/latex]<\/li>\n
    13. [latex]-9\\times -2=18[\/latex]
      \n[latex]-9+-2=-11[\/latex]
      \n[latex]x^2-9xy-2xy+18y^2[\/latex]
      \n[latex]x(x-9y)-2y(x-9y)[\/latex]
      \n[latex](x-9y)(x-2y)[\/latex]<\/li>\n
    14. [latex]-2\\times -7=14[\/latex]
      \n[latex]-2+-7=-9[\/latex]
      \n[latex]u^2-2uv-7uv+14v^2[\/latex]
      \n[latex]u(u-2v)-7v(u-2v)[\/latex]
      \n[latex](u-2v)(u-7v)[\/latex]<\/li>\n
    15. [latex]4\\times -3=-12[\/latex]
      \n[latex]4+-3=1[\/latex]
      \n[latex]x^2+4xy-3xy-12y^2[\/latex]
      \n[latex]x(x+4y)-3y(x+4y)[\/latex]
      \n[latex](x+4y)(x-3y)[\/latex]<\/li>\n
    16. [latex]5\\times 9=45[\/latex]
      \n[latex]5+9=14[\/latex]
      \n[latex]x^2+5xy+9xy+45y^2[\/latex]
      \n[latex]x(x+5y)+9y(x+5y)[\/latex]
      \n[latex](x+5y)(x+9y)[\/latex]<\/li>\n<\/ol>\n","protected":false},"author":90,"menu_order":60,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":"cc-by-nc-sa"},"back-matter-type":[],"contributor":[],"license":[56],"class_list":["post-1899","back-matter","type-back-matter","status-publish","hentry","license-cc-by-nc-sa"],"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1899","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter"}],"about":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/types\/back-matter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1899\/revisions"}],"predecessor-version":[{"id":2217,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1899\/revisions\/2217"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter\/1899\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/media?parent=1899"}],"wp:term":[{"taxonomy":"back-matter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/pressbooks\/v2\/back-matter-type?post=1899"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/contributor?post=1899"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/intermediatealgebraberg\/wp-json\/wp\/v2\/license?post=1899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}