document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178563>Question 1178563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the constant term (x^0) in the expansion of:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281+-+x%5E2+%2B+x%5E3%29+%283x%5E2-%285%2F%287x%5E3%29%29%29%5E6+ ALIGN=MIDDLE  ALT=\"+%281+-+x%5E2+%2B+x%5E3%29+%283x%5E2-%285%2F%287x%5E3%29%29%29%5E6+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807874 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=807874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "DO NOT expand the second factor completely and then multiply the result by the first factor.  That is WAY too much work!<br><BR>\n" );
document.write( "The second factor, when expanded, will contain terms of x^12, x^7, x^2, x^-3, x^-8, x^-13, and x^-18.<br><BR>\n" );
document.write( "The only place where we will get a constant term (x^0) when that factor is multiplied by (1-x^2+x^3) is when the x^3 in the first factor is multiplied by the x^-3 term in the second factor.<br><BR>\n" );
document.write( "The coefficient of the x^-3 term in the expanded second factor is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%286%2C3%29%283%5E3%29%28%28-5%2F7%29%5E3%29+=+%2820%29%2827%29%28-125%2F343%29+=+-67500%2F343 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then the constant term in the completely expanded expression is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%29%28-67500%2F343%29+=+-67500%2F343 ALIGN=MIDDLE  ALT=\"%281%29%28-67500%2F343%29+=+-67500%2F343\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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