document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=694383>Question 694383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the Binomial Theorem to expand the binomial.\r<BR>\n" );
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document.write( "(3v + s)5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #427881 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=427881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at Row 6 in Pascals triangle to see these numbers: 1, 5, 10, 10, 5, 1 \r<BR>\n" );
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document.write( "These coefficients multiply with the following terms:\r<BR>\n" );
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document.write( "(3v)^5*(s)^0<BR>\n" );
document.write( "(3v)^4*(s)^1<BR>\n" );
document.write( "(3v)^3*(s)^2<BR>\n" );
document.write( "(3v)^2*(s)^3<BR>\n" );
document.write( "(3v)^1*(s)^4<BR>\n" );
document.write( "(3v)^0*(s)^5\r<BR>\n" );
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document.write( "So multiply them to get the following\r<BR>\n" );
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document.write( "1*(3v)^5*(s)^0<BR>\n" );
document.write( "5*(3v)^4*(s)^1<BR>\n" );
document.write( "10*(3v)^3*(s)^2<BR>\n" );
document.write( "10*(3v)^2*(s)^3<BR>\n" );
document.write( "5*(3v)^1*(s)^4<BR>\n" );
document.write( "1*(3v)^0*(s)^5\r<BR>\n" );
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document.write( "1*(243v^5)*(1)<BR>\n" );
document.write( "5*(81v^4)*(s)<BR>\n" );
document.write( "10*(27v^3)*(s^2)<BR>\n" );
document.write( "10*(9v^2)*(s^3)<BR>\n" );
document.write( "5*(3v)*(s^4)<BR>\n" );
document.write( "1*(1)*(s^5)\r<BR>\n" );
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document.write( "243v^5<BR>\n" );
document.write( "405sv^4<BR>\n" );
document.write( "270s^2v^3<BR>\n" );
document.write( "90s^3v^2<BR>\n" );
document.write( "15s^4v<BR>\n" );
document.write( "s^5\r<BR>\n" );
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document.write( "Then add up all the terms to get this final answer\r<BR>\n" );
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document.write( "243v^5 + 405sv^4 + 270s^2v^3 + 90s^3v^2 + 15s^4v + s^5\r<BR>\n" );
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document.write( "So\r<BR>\n" );
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document.write( "(3v+s)^5 = 243v^5 + 405sv^4 + 270s^2v^3 + 90s^3v^2 + 15s^4v + s^5\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );