document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170629>Question 1170629</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, can help me solve this? Thankss~<BR>\n" );
document.write( "(a) Find the term that is independent of x in the expansion of (x - 3/x)^6 in ascending powers of x.<BR>\n" );
document.write( "(b) Hence, 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 #795524 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=795524\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "a.\r<BR>\n" );
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document.write( "Find the term that is independent of x in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%2Fx%29%5E6 ALIGN=MIDDLE  ALT=\"%28x+-+3%2Fx%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "Formula to use \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28nCm%29%28a%5E%28n-m%29%29%28b%5Em%29 ALIGN=MIDDLE  ALT=\"%28nCm%29%28a%5E%28n-m%29%29%28b%5Em%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%2Fx%29%5E6 ALIGN=MIDDLE  ALT=\"%28x+-+3%2Fx%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+x ALIGN=MIDDLE  ALT=\"a+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-3%2Fx ALIGN=MIDDLE  ALT=\"b+=+-3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+6 ALIGN=MIDDLE  ALT=\"n+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286Cm%29%28x%5E%286-m%29%29%2A%28-3%2Fx%29%5Em%0D%0A%7B%7B%7Br ALIGN=MIDDLE  ALT=\"%286Cm%29%28x%5E%286-m%29%29%2A%28-3%2Fx%29%5Em%0D%0A%7B%7B%7Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286Cm%29%28-3%29%5Em%2A%28x%5E%286-2m%29%29%0D%0A%0D%0ALet+%7B%7B%7B%286Cm%29%28-3%29%5Em=K%5Bj%5D ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term involving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5B1%5Dx%5E0 ALIGN=MIDDLE  ALT=\"K%5B1%5Dx%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2m=0 ALIGN=MIDDLE  ALT=\"6-2m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5B1%5D=%286C3%29%28-3%29%5E3=-540 ALIGN=MIDDLE  ALT=\"K%5B1%5D=%286C3%29%28-3%29%5E3=-540\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "check expanded form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E6+%2B+729%2Fx%5E6+-+18+x%5E4+-+1458%2Fx%5E4+%2B+135+x%5E2+%2B+1215%2Fx%5E2+-+540 ALIGN=MIDDLE  ALT=\"x%5E6+%2B+729%2Fx%5E6+-+18+x%5E4+-+1458%2Fx%5E4+%2B+135+x%5E2+%2B+1215%2Fx%5E2+-+540\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b. Hence, find the term that is independent of x in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2B2%2Fx%5E2%29%28x-3%2Fx%29%5E6 ALIGN=MIDDLE  ALT=\"%282%2B2%2Fx%5E2%29%28x-3%2Fx%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Find the term that is independent of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > in the expansion of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%2B2%2Fx%5E2%29%28x-3%2Fx%29%5E6 ALIGN=MIDDLE  ALT=\"+%282%2B2%2Fx%5E2%29%28x-3%2Fx%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Formula to use \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28nCm%29%28a%5E%28n-m%29%29%28b%5Em%29 ALIGN=MIDDLE  ALT=\"%28nCm%29%28a%5E%28n-m%29%29%28b%5Em%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "For <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+3%2Fx%29%5E6 ALIGN=MIDDLE  ALT=\"%28x+-+3%2Fx%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+x ALIGN=MIDDLE  ALT=\"a+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-3%2Fx ALIGN=MIDDLE  ALT=\"b+=+-3%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+=+6 ALIGN=MIDDLE  ALT=\"n+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286Cm%29%28x%5E%286-m%29%29%2A%28-3%2Fx%29%5Em%0D%0A%7B%7B%7Br ALIGN=MIDDLE  ALT=\"%286Cm%29%28x%5E%286-m%29%29%2A%28-3%2Fx%29%5Em%0D%0A%7B%7B%7Br\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286Cm%29%28-3%29%5Em%2A%28x%5E%286-2m%29%29%0D%0A%0D%0ALet+%7B%7B%7B%286Cm%29%28-3%29%5Em=K%5Bj%5D ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term involving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5B1%5Dx%5E0 ALIGN=MIDDLE  ALT=\"K%5B1%5Dx%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2m=0 ALIGN=MIDDLE  ALT=\"6-2m=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=3 ALIGN=MIDDLE  ALT=\"m=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5B1%5D=%286C3%29%28-3%29%5E3=-540 ALIGN=MIDDLE  ALT=\"K%5B1%5D=%286C3%29%28-3%29%5E3=-540\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term involving <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5B2%5Dx%5E2 ALIGN=MIDDLE  ALT=\"K%5B2%5Dx%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2m=2 ALIGN=MIDDLE  ALT=\"6-2m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=2 ALIGN=MIDDLE  ALT=\"m=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%5B2%5D=%286C2%29%28-3%29%5E2=135 ALIGN=MIDDLE  ALT=\"K%5B2%5D=%286C2%29%28-3%29%5E2=135\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "The constant term in the expansion of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282+%2B+2%2Fx%5E2%29%28x+-+3%2Fx%29%5E6 ALIGN=MIDDLE  ALT=\"+%282+%2B+2%2Fx%5E2%29%28x+-+3%2Fx%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=2K%5B1%5D%2B2K%5B2%5D=2%28-540%29%2B2%28135%29 ALIGN=MIDDLE  ALT=\"K=2K%5B1%5D%2B2K%5B2%5D=2%28-540%29%2B2%28135%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=+-810 ALIGN=MIDDLE  ALT=\"K=+-810\"   DISABLED_style= \"max-width:90%; height:auto;\" >←   answer\r<BR>\n" );
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document.write( "expanded form:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1458%2Fx%5E8+%2B+2x%5E6+-+1458%2Fx%5E6+-+34x%5E4+-+486%2Fx%5E4+%2B+234x%5E2+%2B+1350%2Fx%5E2+-+810 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );