document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1030211>Question 1030211</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B+mx%5E2+%2B+n ALIGN=MIDDLE  ALT=\"%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B+mx%5E2+%2B+n\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "for integers a, b, m and n, what is the product of m and n?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #645095 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=645095\">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=%28x%5E2+%2B+3x+%2B+6%29%28x%5E2+%2B+ax+%2B+b%29+=+x%5E4+%2B%28a%2B3%29x%5E3+%2B+%28b%2B3a%2B6%29x%5E2+%2B+%283b+%2B6a%29x+%2B+6b+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > after expansion.  This is supposed to be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E4+%2B+mx%5E2+%2B+n ALIGN=MIDDLE  ALT=\"+x%5E4+%2B+mx%5E2+%2B+n\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "\n" );
document.write( "By equating coefficients, we obtain...<BR>\n" );
document.write( "==> a+3 = 0,<BR>\n" );
document.write( "m = b+3a+6,<BR>\n" );
document.write( "3b+6a = 0, or b+2a = 0 after reduction,<BR>\n" );
document.write( "6b = n\r<BR>\n" );
document.write( "\n" );
document.write( "==> a = -3,<BR>\n" );
document.write( "b = 6,<BR>\n" );
document.write( "m = 6 - 9 +6 = 3, and <BR>\n" );
document.write( "n = 6*6 = 36\r<BR>\n" );
document.write( "\n" );
document.write( "==> mn = 3*36 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28108%29 ALIGN=MIDDLE  ALT=\"highlight%28108%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );