document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=261557>Question 261557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Finds the coefficient of x^2 in the expansion of (x + (2/radical x))^8 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #192721 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=192721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Finds the coefficient of x^2 in the expansion of (x + (2/radical x))^8<BR>\n" );
document.write( "------------------<BR>\n" );
document.write( "(x + 2x^-1)^8<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "Examine (x)^k(2x^(-1))^(n-k) = x^2<BR>\n" );
document.write( "(x^k)(x^(k-n)) = x^2<BR>\n" );
document.write( "x^(2k-n) = x^2<BR>\n" );
document.write( "2k-n = 2<BR>\n" );
document.write( "n = 2k-2<BR>\n" );
document.write( "------------------------------<BR>\n" );
document.write( "8C8(x^0)(2x^-1)^8 = x^-8<BR>\n" );
document.write( "8C7(x^1)(2x^-1)^7 = x^-6<BR>\n" );
document.write( "8C6(x^2)(2x^-1)^6 = x^-2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "8C5(x^3)(2x^-1)^5 = x<BR>\n" );
document.write( "8C3(x^5)(2x^-1)^3 = 8x^2<BR>\n" );
document.write( "...<BR>\n" );
document.write( "8C1(x^2)^7(2x^-1)^1 = x^1<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "Ans: 8<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );