document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=654549>Question 654549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Algebra help!! (2x-3)^4 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408764 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=408764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Look at Row 5 in Pascals triangle: 1, 4, 6, 4, 1 \r<BR>\n" );
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document.write( "These are the coefficients to the terms\r<BR>\n" );
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document.write( "(2x)^4*(-3)^0<BR>\n" );
document.write( "(2x)^3*(-3)^1<BR>\n" );
document.write( "(2x)^2*(-3)^2<BR>\n" );
document.write( "(2x)^1*(-3)^3<BR>\n" );
document.write( "(2x)^0*(-3)^4\r<BR>\n" );
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document.write( "Note: you basically raise the first piece to the 4th power and the second piece to the 0th power. Then you count down on the first exponent and count up on the second exponent.\r<BR>\n" );
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document.write( "so we get \r<BR>\n" );
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document.write( "1*(2x)^4*(-3)^0<BR>\n" );
document.write( "4*(2x)^3*(-3)^1<BR>\n" );
document.write( "6*(2x)^2*(-3)^2<BR>\n" );
document.write( "4*(2x)^1*(-3)^3<BR>\n" );
document.write( "1*(2x)^0*(-3)^4\r<BR>\n" );
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document.write( "which simplifies to\r<BR>\n" );
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document.write( "1*(16x^4)*(1)<BR>\n" );
document.write( "4*(8x^3)*(-3)<BR>\n" );
document.write( "6*(4x^2)*(9)<BR>\n" );
document.write( "4*(2x^1)*(-27)<BR>\n" );
document.write( "1*(1)*(81)\r<BR>\n" );
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document.write( "and that simplifies to\r<BR>\n" );
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document.write( "16x^4<BR>\n" );
document.write( "-96x^3<BR>\n" );
document.write( "216x^2<BR>\n" );
document.write( "-216x<BR>\n" );
document.write( "81\r<BR>\n" );
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document.write( "Now add up the terms to get \r<BR>\n" );
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document.write( "16x^4 - 96x^3 + 216x^2 - 216x + 81\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "(2x-3)^4 = 16x^4 - 96x^3 + 216x^2 - 216x + 81 for all values of x\r<BR>\n" );
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