document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158319>Question 1158319</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Explain how to find the fifth term of the expansion of (2x+3y)^9 without writing out the entire sequence.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781235 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</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=781235\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Picture the expression as 9 factors of (2x+3y) being multiplied together.<br><BR>\n" );
document.write( "The first term in the product will use the x term from all 9 factors;<BR>\n" );
document.write( "The second term will use the x term 8 times and the y term 1 time;<BR>\n" );
document.write( "...<BR>\n" );
document.write( "The fifth term will use the x term 5 times and the y term 4 times.<br><BR>\n" );
document.write( "The first part in the calculation of the fifth term is determining the number of different ways you can choose 5 of the 9 factors to be the ones in which the x term is chosen.  That number of ways is \"9 choose 5\":<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%289%2C5%29+=+9%21%2F%28%285%21%29%289-5%29%21%29+=+%289%2A8%2A7%2A6%29%2F%284%2A3%2A2%2A1%29+=+84 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "In each of those 84 cases, the (2x) factor is used 5 times and the (3y) factor is used 4 times.<br><BR>\n" );
document.write( "So the fifth term in the expansion is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2884%29%28%282x%29%5E5%29%28%283y%29%5E4%29 ALIGN=MIDDLE  ALT=\"%2884%29%28%282x%29%5E5%29%28%283y%29%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2884%29%282%5E5%29%283%5E4%29%29x%5E5y%5E4 ALIGN=MIDDLE  ALT=\"%28%2884%29%282%5E5%29%283%5E4%29%29x%5E5y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use a calculator if you need to multiply all that out.<br><BR>\n" );
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