document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7131>Question 7131</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to learn, with great difficulty, how to factor this type of problem... 2a^2-2ab-24b^2 ... I have tried factoring out the 2, but I don't know how to go any further with this problem.  How do I find the factors of 12 if there is no factor for the prceding term?  Thank you so much for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3942 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=3942\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Well, you could start by factoring a 2 from the expression, just to simplify it a bit.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2+-+2ab+-+24b%5E2 ALIGN=MIDDLE  ALT=\"2a%5E2+-+2ab+-+24b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28a%5E2+-+ab+-+12b%5E2%29 ALIGN=MIDDLE  ALT=\"2%28a%5E2+-+ab+-+12b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's look at the expression in the parentheses: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+ab+-+12b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-+ab+-+12b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The factors of the first term , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%29%28a%29 ALIGN=MIDDLE  ALT=\"%28a%29%28a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Look at the last term: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12b%5E2 ALIGN=MIDDLE  ALT=\"-12b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and ask what are the factors of this term?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-12b%5E2 ALIGN=MIDDLE  ALT=\"-12b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283b%29%28-4b%29 ALIGN=MIDDLE  ALT=\"%283b%29%28-4b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-3b%29%284b%29 ALIGN=MIDDLE  ALT=\"%28-3b%29%284b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > just to name a couple.\r<BR>\n" );
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document.write( "So, now try: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B+3b%29%28a+-+4b%29 ALIGN=MIDDLE  ALT=\"%28a+%2B+3b%29%28a+-+4b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Using the FOIL method, multiply these factors:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B+3b%29%28a+-+4b%29+=+%28a%5E2+-+4ab+%2B+3ab+-+12b%5E2%29 ALIGN=MIDDLE  ALT=\"%28a+%2B+3b%29%28a+-+4b%29+=+%28a%5E2+-+4ab+%2B+3ab+-+12b%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+ab+-+12b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-+ab+-+12b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and if you multiply by the 2 we factored at the start, we'll get:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%5E2+-+2ab+-+24b%5E2 ALIGN=MIDDLE  ALT=\"2a%5E2+-+2ab+-+24b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the factors are: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28a%2B3b%29%28a-4b%29 ALIGN=MIDDLE  ALT=\"2%28a%2B3b%29%28a-4b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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