document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=42556>Question 42556</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7.\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 #27670 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27670\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The r-th term in the binomial expansion of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+%2B+x%29%5En ALIGN=MIDDLE  ALT=\"%28a+%2B+x%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > for positive integral values of 'n' is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5Br%5D+=+nC%5Br%5D%2Aa%5E%28n-r%29%2Ax%5Er ALIGN=MIDDLE  ALT=\"t%5Br%5D+=+nC%5Br%5D%2Aa%5E%28n-r%29%2Ax%5Er\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here, a = m, x = 2p, n = 7.<BR>\n" );
document.write( "For the 6th term, r = 6.<BR>\n" );
document.write( "So replace a, x, n and r in the formula of r-th term and get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B6%5D+=+7C%5B6%5D%2Am%5E%287-6%29%2A%282a%29%5E6 ALIGN=MIDDLE  ALT=\"t%5B6%5D+=+7C%5B6%5D%2Am%5E%287-6%29%2A%282a%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B6%5D+=+2%5E6%2A7C%5B6%5D%2Am%5E1a%5E6 ALIGN=MIDDLE  ALT=\"t%5B6%5D+=+2%5E6%2A7C%5B6%5D%2Am%5E1a%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7C%5B6%5D+=+7%21%2F%286%21%287-6%29%21%29 ALIGN=MIDDLE  ALT=\"7C%5B6%5D+=+7%21%2F%286%21%287-6%29%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%21%2F%286%211%21%29 ALIGN=MIDDLE  ALT=\"7%21%2F%286%211%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%21%2A7%29%2F%286%21%2A1%29 ALIGN=MIDDLE  ALT=\"%286%21%2A7%29%2F%286%21%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7.\r<BR>\n" );
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document.write( "Hence the reqd 6th term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%5B6%5D+=+2%5E6%2A7%2Ama%5E6 ALIGN=MIDDLE  ALT=\"t%5B6%5D+=+2%5E6%2A7%2Ama%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A7%2Ama%5E6 ALIGN=MIDDLE  ALT=\"64%2A7%2Ama%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=448ma%5E6 ALIGN=MIDDLE  ALT=\"448ma%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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