document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=60905>Question 60905</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Fully Factor. \r<BR>\n" );
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document.write( "1. 3a^2-36a+36<BR>\n" );
document.write( "2. 4(x-3)^2 - 9(x+4)^2\r<BR>\n" );
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document.write( "Help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #41861 by </B><A HREF=/tutors/aboutme.mpl?userid=joyofmath><B>joyofmath(189)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=joyofmath><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=41861\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3a%5E2-36a%2B36 ALIGN=MIDDLE  ALT=\"3a%5E2-36a%2B36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 3.<BR>\n" );
document.write( "Then you get  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28a%5E2-12a%2B12%29 ALIGN=MIDDLE  ALT=\"3%28a%5E2-12a%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > which doesn't factor any more.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x-3%29%5E2+-+9%28x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"4%28x-3%29%5E2+-+9%28x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and let B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then the expression is this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A%5E2-9B%5E2 ALIGN=MIDDLE  ALT=\"4A%5E2-9B%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4A%5E2+=+%282A%29%5E2 ALIGN=MIDDLE  ALT=\"4A%5E2+=+%282A%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9B%5E2+=+%283B%29%5E2 ALIGN=MIDDLE  ALT=\"9B%5E2+=+%283B%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the expression becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282A%29%5E2-%283B%29%5E2 ALIGN=MIDDLE  ALT=\"%282A%29%5E2-%283B%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is a difference of two squares. \r<BR>\n" );
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document.write( "It's useful to recognize that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%28x-y%29 ALIGN=MIDDLE  ALT=\"%28x%2By%29%28x-y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, our expression becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282A%2B3B%29%282A-3B%29 ALIGN=MIDDLE  ALT=\"%282A%2B3B%29%282A-3B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, plug in A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3 ALIGN=MIDDLE  ALT=\"x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and B = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B4 ALIGN=MIDDLE  ALT=\"x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the expression.\r<BR>\n" );
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document.write( "You get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%28x-3%29%2B3%28x%2B4%29%29%282%28x-3%29-3%28x%2B4%29%29 ALIGN=MIDDLE  ALT=\"%282%28x-3%29%2B3%28x%2B4%29%29%282%28x-3%29-3%28x%2B4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply things out to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-6%2B3x%2B12%29%282x-6-3x-12%29 ALIGN=MIDDLE  ALT=\"%282x-6%2B3x%2B12%29%282x-6-3x-12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Collect like terms and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B6%29%28-x-18%29 ALIGN=MIDDLE  ALT=\"%285x%2B6%29%28-x-18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It's nice to move the minus sign out of the equation.\r<BR>\n" );
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document.write( "The answer then is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%285x%2B6%29%28x%2B18%29 ALIGN=MIDDLE  ALT=\"-%285x%2B6%29%28x%2B18%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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