document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=109879>Question 109879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor completely.    b2 – ab – 6a2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #80079 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=80079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First off, what two numbers multiply to -6 (the last coefficient) but add to -1 (the middle coefficient)? It turns out that -3 and 2 multiply to -6 but add to -1.\r<BR>\n" );
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document.write( "So replace the middle term of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3ab%2B2ab ALIGN=MIDDLE  ALT=\"-3ab%2B2ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-3ab%2B2ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-3ab%2B2ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now let's factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-3ab%2B2ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-3ab%2B2ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > by grouping\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%5E2-3ab%29%2B%282ab-6a%5E2%29 ALIGN=MIDDLE  ALT=\"%28b%5E2-3ab%29%2B%282ab-6a%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%28b-3a%29%2B2a%28b-3a%29 ALIGN=MIDDLE  ALT=\"b%28b-3a%29%2B2a%28b-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the first group. Factor out the GCF of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a ALIGN=MIDDLE  ALT=\"2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > out of the second group\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B2a%29%28b-3a%29 ALIGN=MIDDLE  ALT=\"%28b%2B2a%29%28b-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we have a common term of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%2B-3a ALIGN=MIDDLE  ALT=\"b%2B-3a\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can combine like terms\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-3ab%2B2ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-3ab%2B2ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B2a%29%28b-3a%29 ALIGN=MIDDLE  ALT=\"%28b%2B2a%29%28b-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "This means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B2a%29%28b-3a%29 ALIGN=MIDDLE  ALT=\"%28b%2B2a%29%28b-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > also\r<BR>\n" );
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document.write( "Notice how <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b%2B2a%29%28b-3a%29 ALIGN=MIDDLE  ALT=\"%28b%2B2a%29%28b-3a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > foils back to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-3ab%2B2ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-3ab%2B2ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-ab-6a%5E2 ALIGN=MIDDLE  ALT=\"b%5E2-ab-6a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer.<BR>\n" );
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