document.write( "Question 1031691: What is the coefficient of x in (x^4 + x^3 + x^2 + x + 1)^4? \n" ); document.write( "
Algebra.Com's Answer #646381 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\"%28x%5E4+%2B+x%5E3+%2B+x%5E2+%2B+x+%2B+1%29%5E4\"\"%22%22=%22%22\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The only way to get a x in that multiplication is: \r\n" );
document.write( "\r\n" );
document.write( "1. When the 1's in the 1st, 2nd, and 3rd parentheses are multiplied \r\n" );
document.write( "   by the x in the 4th parentheses, giving term 1*1*1*x = x.\r\n" );
document.write( "\r\n" );
document.write( "2. When the 1's in the 1st, 2nd, and 4th parentheses are multiplied \r\n" );
document.write( "   by the x in the 3rd parentheses, giving term 1*1*x*1 = x.\r\n" );
document.write( "\r\n" );
document.write( "3. When the 1's in the 1st, 3rd, and 4th parentheses are multiplied \r\n" );
document.write( "   by the x in the 2nd parentheses, giving term 1*x*1*1 = x.\r\n" );
document.write( "\r\n" );
document.write( "4. When the 1's in the 2nd, 3rd, and 4th parentheses are multiplied \r\n" );
document.write( "   by the x in the 1st parentheses, giving term x*1*1*1 = x.\r\n" );
document.write( "\r\n" );
document.write( "So the only term in x is x+x+x+x = 4x, which has coefficient 4.\r\n" );
document.write( "\r\n" );
document.write( "Incidentally, the whole thing multiplied out is:\r\n" );
document.write( "\r\n" );
document.write( "x16+4x15+10x14+20x13+35x12+52x11+68x10+80x9+85x8+80x7+68x6+52x5+35x4+20x3+10x2+4x+1\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );