document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=78114>Question 78114</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Factor the polynomials completely,Show the GCF\r<BR>\n" );
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document.write( "25x^2+36y^2\r<BR>\n" );
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document.write( "I got..<BR>\n" );
document.write( "(5x+6y)(5x+6y) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #56026 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=56026\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Factor:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2%2B36y%5E2 ALIGN=MIDDLE  ALT=\"25x%5E2%2B36y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > This is not factorable.<BR>\n" );
document.write( "Your answer doesn't work and you can readily see this when you multiply the factors (using FOIL) that you obtained.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B6y%29%285x%2B6y%29+=+25x%5E2%2B30xy%2B30xy%2B36y%5E2 ALIGN=MIDDLE  ALT=\"%285x%2B6y%29%285x%2B6y%29+=+25x%5E2%2B30xy%2B30xy%2B36y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying this, you get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2%2B60xy%2B36y%5E2 ALIGN=MIDDLE  ALT=\"25x%5E2%2B60xy%2B36y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If you have studied complex numbers in your math course, then you can write the factors of the given expression as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2%2B36y%5E2+=+%285x%2B6yi%29%285x-6yi%29 ALIGN=MIDDLE  ALT=\"25x%5E2%2B36y%5E2+=+%285x%2B6yi%29%285x-6yi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i+=+sqrt%28-1%29 ALIGN=MIDDLE  ALT=\"i+=+sqrt%28-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let's multiply the factors and see what we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285x%2B6yi%29%285x-6yi%29+=+25x%5E2%2B30xyi-30xyi-36y%5E2%28i%5E2%29 ALIGN=MIDDLE  ALT=\"%285x%2B6yi%29%285x-6yi%29+=+25x%5E2%2B30xyi-30xyi-36y%5E2%28i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying this, we get:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2-36y%5E2%28i%5E2%29 ALIGN=MIDDLE  ALT=\"25x%5E2-36y%5E2%28i%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but, recall that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=i%5E2+=+-1 ALIGN=MIDDLE  ALT=\"i%5E2+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2-36y%5E2%28-1%29+=+25x%5E2%2B36y%5E2 ALIGN=MIDDLE  ALT=\"25x%5E2-36y%5E2%28-1%29+=+25x%5E2%2B36y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Does this make sense to you? </SPAN>\n" );
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