document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374965>Question 374965</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (5&#8730;6-15&#8730;3)(4&#8730;6+12&#8730;3)  Can someone help me with this. The instructions say to simplify. Type an exact answer using radicals as needed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266654 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266654\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "There are a couple of ways to skin this cat.  The first way is just to use FOIL and go at it straight on.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(5\sqrt{6}\ -\ 15\sqrt{3}\right)\left(4\sqrt{6}\ -\ 12\sqrt{3}\right)\ =\ 20\,\cdot\,6\ +\ 60\sqrt{18}\ -\ 60\sqrt{18}\ -\ 180\,\cdot\,3\ =\ -420\">\r<BR>\n" );
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document.write( "Or notice that the first binomial has a 5 that you can factor out and the second binomial has a 4 that you can factor out:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5\,\cdot\,\left(\sqrt{6}\ -\ 3\sqrt{3}\right)\,\cdot\,4\,\cdot\,\left(\sqrt{6}\ -\ 3\sqrt{3}\right)\">\r<BR>\n" );
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document.write( "Now notice that the remaining binomial factors are a conjugate pair, hence the product is the difference of two squares:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 5\ \cdot\ 4\ \left(\sqrt{6}\ -\ 3\sqrt{3}\right)\left(\sqrt{6}\ +\ 3\sqrt{3}\right)\ =\ 20\ \cdot\ (6\ -\ 27)\ =\ -420\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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