document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170639>Question 1170639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the term that is independent of x in the expansion of (2+2/x^2)(x-3/x)^6. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #795541 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=795541\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The expansion of the second factor will be in the form<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Ax%5E6%2BBx%5E4%2BCx%5E2%2BD%2BE%2Fx%5E2%2BF%2Fx%5E4%2BG%2Fx%5E6 ALIGN=MIDDLE  ALT=\"Ax%5E6%2BBx%5E4%2BCx%5E2%2BD%2BE%2Fx%5E2%2BF%2Fx%5E4%2BG%2Fx%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "When that is multiplied by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2B2%2Fx%5E2 ALIGN=MIDDLE  ALT=\"2%2B2%2Fx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will get constant partial products from two places: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28D%29%282%29 ALIGN=MIDDLE  ALT=\"%28D%29%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Cx%5E2%29%282%2Fx%5E2%29 ALIGN=MIDDLE  ALT=\"%28Cx%5E2%29%282%2Fx%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the constant term in the final expansion will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2C%2B2D ALIGN=MIDDLE  ALT=\"2C%2B2D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So we need to calculate the coefficients of the constant and x^2 terms, C and D.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+C%286%2C3%29%28%281%5E3%29%28%28-3%29%5E3%29%29+=+%2820%29%281%29%28-27%29+=+-540 ALIGN=MIDDLE  ALT=\"D+=+C%286%2C3%29%28%281%5E3%29%28%28-3%29%5E3%29%29+=+%2820%29%281%29%28-27%29+=+-540\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+C%286%2C4%29%28%281%5E4%29%28%28-3%29%5E2%29%29+=+%2815%29%281%29%289%29+=+135 ALIGN=MIDDLE  ALT=\"C+=+C%286%2C4%29%28%281%5E4%29%28%28-3%29%5E2%29%29+=+%2815%29%281%29%289%29+=+135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2C%2B2D+=+2%28C%2BD%29+=+2%28-540%2B135%29+=+2%28-405%29+=+-810 ALIGN=MIDDLE  ALT=\"2C%2B2D+=+2%28C%2BD%29+=+2%28-540%2B135%29+=+2%28-405%29+=+-810\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: -810<br><BR>\n" );
document.write( " </SPAN>\n" );
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