document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=309970>Question 309970</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help to find the product of each pair of conjugates.\r<BR>\n" );
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document.write( "(2sqrt3 - sqrt7)(2sqrt3 + sqrt7) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #221706 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=221706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%287%29 ALIGN=MIDDLE  ALT=\"y=sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%28x%2By%29 ALIGN=MIDDLE  ALT=\"%28x-y%29%28x%2By%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. FOILing this expression gives us <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-y%29%28x%2By%29=x%5E2-y%5E2 ALIGN=MIDDLE  ALT=\"%28x-y%29%28x%2By%29=x%5E2-y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is a difference of squares. Plug <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x=2%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%287%29 ALIGN=MIDDLE  ALT=\"y=sqrt%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > back in to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=%282%2Asqrt%283%29%29%5E2-%28sqrt%287%29%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Now just multiply out and simplify the right side to get: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=4%2A3-7 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=4%2A3-7\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and do a bit more arithmetic to get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=5 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%283%29-sqrt%287%29%29%282%2Asqrt%283%29%2Bsqrt%287%29%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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