document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=358123>Question 358123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> multiply\r<BR>\n" );
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document.write( "( 2sqrt(3) - 4sqrt(6) )( 3sqrt(3) + 6sqrt(6) ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255755 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=255755\">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=%28+2sqrt%283%29+-+4sqrt%286%29+%29%28+3sqrt%283%29+%2B+6sqrt%286%29+%29 ALIGN=MIDDLE  ALT=\"%28+2sqrt%283%29+-+4sqrt%286%29+%29%28+3sqrt%283%29+%2B+6sqrt%286%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This expression is similar to<BR>\n" );
document.write( "(2x - 3y)(3x + 6y)<BR>\n" );
document.write( "and we do the same thing to multiply: Use FOIL (or whatever technique you have learned to multiply polynomials):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%283%29%2A3sqrt%283%29+%2B+2sqrt%283%29%2A6sqrt%286%29+-4sqrt%286%293sqrt%283%29+-4sqrt%286%296sqrt%286%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Within each product we will multiply the coefficients and use the property of radicals, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29 ALIGN=MIDDLE  ALT=\"root%28a%2C+p%29%2Aroot%28a%2C+q%29+=+root%28a%2C+p%2Aq%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, to multiply the square roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6sqrt%283%2A3%29+%2B+12sqrt%283%2A6%29+-12sqrt%286%2A3%29+-24sqrt%286%2A6%29 ALIGN=MIDDLE  ALT=\"6sqrt%283%2A3%29+%2B+12sqrt%283%2A6%29+-12sqrt%286%2A3%29+-24sqrt%286%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies as follows:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6sqrt%289%29+%2B+12sqrt%2818%29+-12sqrt%2818%29+-24sqrt%2836%29 ALIGN=MIDDLE  ALT=\"6sqrt%289%29+%2B+12sqrt%2818%29+-12sqrt%2818%29+-24sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29+=+3 ALIGN=MIDDLE  ALT=\"sqrt%289%29+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29+=+6 ALIGN=MIDDLE  ALT=\"sqrt%2836%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and since the two middle terms cancel out:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A3+-24%2A6 ALIGN=MIDDLE  ALT=\"6%2A3+-24%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18+-+144 ALIGN=MIDDLE  ALT=\"18+-+144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-126 ALIGN=MIDDLE  ALT=\"-126\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28+2sqrt%283%29+-+4sqrt%286%29+%29%28+3sqrt%283%29+%2B+6sqrt%286%29+%29+=+-126 ALIGN=MIDDLE  ALT=\"%28+2sqrt%283%29+-+4sqrt%286%29+%29%28+3sqrt%283%29+%2B+6sqrt%286%29+%29+=+-126\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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