document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203588>Question 1203588</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the coefficient of the 5th term of the expansion of (2x^2 + 3y^3)^10 how about the sum of exponents of the terms in expansion\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839264 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=839264\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "To find the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2%2B+3y%5E3%29%5E10 ALIGN=MIDDLE  ALT=\"%282x%5E2%2B+3y%5E3%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we need to use the binomial theorem. \r<BR>\n" );
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document.write( "The general term in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2%2B+3y%5E3%29%5E10 ALIGN=MIDDLE  ALT=\"%282x%5E2%2B+3y%5E3%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%28r%2B1%29+=+C%2810%2C+r%29+%2A+%282x%5E2%29%5E%2810-r%29+%2A+%283y%5E3%29%5Er ALIGN=MIDDLE  ALT=\"T%28r%2B1%29+=+C%2810%2C+r%29+%2A+%282x%5E2%29%5E%2810-r%29+%2A+%283y%5E3%29%5Er\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2810%2C+r%29 ALIGN=MIDDLE  ALT=\"C%2810%2C+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the binomial coefficient of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >, given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2810%2C+r%29+=+10%21+%2F+%28r%21+%2A+%2810+-+r%29%21%29 ALIGN=MIDDLE  ALT=\"C%2810%2C+r%29+=+10%21+%2F+%28r%21+%2A+%2810+-+r%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "To find the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term, we need to substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+4 ALIGN=MIDDLE  ALT=\"r+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since the first term has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+0 ALIGN=MIDDLE  ALT=\"r+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Therefore, the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T%285%29+=+C%2810%2C+4%29+%2A+%282x%5E2%29%5E%2810-4%29+%2A+%283y%5E3%29%5E4 ALIGN=MIDDLE  ALT=\"T%285%29+=+C%2810%2C+4%29+%2A+%282x%5E2%29%5E%2810-4%29+%2A+%283y%5E3%29%5E4\"   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=C%2810%2C+4%29+%2A+%282x%5E2%29%5E6+%2A+%283y%5E3%29%5E4 ALIGN=MIDDLE  ALT=\"C%2810%2C+4%29+%2A+%282x%5E2%29%5E6+%2A+%283y%5E3%29%5E4\"   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=210+%2A+64x%5E12+%2A+81y%5E12 ALIGN=MIDDLE  ALT=\"210+%2A+64x%5E12+%2A+81y%5E12\"   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=1088640x%5E12%2Ay%5E12 ALIGN=MIDDLE  ALT=\"1088640x%5E12%2Ay%5E12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the coefficient of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" >th term in the expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%5E2+%2B+3y%5E3%29%5E10 ALIGN=MIDDLE  ALT=\"%282x%5E2+%2B+3y%5E3%29%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1088640 ALIGN=MIDDLE  ALT=\"1088640\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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