document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109181>Question 1109181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Expand completely (2x3+1)5 </SPAN>\n" );
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document.write( "Multiplying the expression times itself 5 times is inefficient.  Use the binomial theorem.<br><BR>\n" );
document.write( "(2x^3+1)^5<BR>\n" );
document.write( " = C(5,5)*(2x^3)^5*(1)^0<BR>\n" );
document.write( " + C(5,4)*(2x^3)^4*(1)^1<BR>\n" );
document.write( " + C(5,3)*(2x^3)^3*(1)^2<BR>\n" );
document.write( " + C(5,2)*(2x^3)^2*(1)^3<BR>\n" );
document.write( " + C(5,1)*(2x^3)^1*(1)^4)<BR>\n" );
document.write( " + C(5,0)*(2x^3)^0*(1)^5<br><BR>\n" );
document.write( " = 1(2x^3)^5 + 5(2x^3)^4 + 10(2x^3)^3 + 10(2x^3)^2 + 5(2x^3)^1 + 1(2x^3)^0<br><BR>\n" );
document.write( " = 32x^15 + 5*16x^12 + 10*8x^9 + 10*4x^6 + 5*2x^3 + 1<br><BR>\n" );
document.write( " = 32x^15 + 80x^12 + 80x^9 + 40x^6 + 10x^3 + 1 </SPAN>\n" );
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