document.write( "Question 49212: Expand Problems using the binomial formula\r
\n" ); document.write( "\n" ); document.write( "(2x-y)^6\r
\n" ); document.write( "\n" ); document.write( "Thank you, Michelle
\n" ); document.write( "

Algebra.Com's Answer #32638 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
(2x-y)6 \r\n" );
document.write( "\r\n" );
document.write( "Since the exponent is 6 there will be one \r\n" );
document.write( "more than 6 terms, or 7 terms.  They are:\r\n" );
document.write( "\r\n" );
document.write( "C(6,6)(2x)6(-y)0 +\r\n" );
document.write( "C(6,5)(2x)5(-y)1 + \r\n" );
document.write( "C(6,4)(2x)4(-y)2 + \r\n" );
document.write( "C(6,3)(2x)3(-y)3 +\r\n" );
document.write( "C(6,2)(2x)2(-y)4 + \r\n" );
document.write( "C(6,1)(2x)1(-y)5 + \r\n" );
document.write( "C(6,0)(2x)0(-y)6  \r\n" );
document.write( "\r\n" );
document.write( "Study the formation of the above 7 terms. \r\n" );
document.write( "Notice that each of the 7 terms is of this\r\n" );
document.write( "form:\r\n" );
document.write( "\r\n" );
document.write( "C(6,_)(2x)¯(-y)¯\r\n" );
document.write( "\r\n" );
document.write( "The first two blanks are the same, they start \r\n" );
document.write( "with 6 and go down to 0 and the last blank \r\n" );
document.write( "starts at 0 and goes up to 6\r\n" );
document.write( "\r\n" );
document.write( "I will assume you understand how to calculate\r\n" );
document.write( "the binomial coefficients using this formula:\r\n" );
document.write( "\r\n" );
document.write( "             n!\r\n" );
document.write( "C(n,r) = ----------\r\n" );
document.write( "          r!(n-r)!\r\n" );
document.write( "\r\n" );
document.write( "where M! = M(M-1)(M-2)···3·2·1\r\n" );
document.write( "\r\n" );
document.write( "If you don't understand that, post again.\r\n" );
document.write( "Maybe your book uses nCr\r\n" );
document.write( "instead but if so, it's the same as C(n,r)\r\n" );
document.write( "\r\n" );
document.write( "C(6,6)(2x)6(-y)0 =  1(26x6)(-y)0 = 1(64)x6(1) = 64x6\r\n" );
document.write( "C(6,5)(2x)5(-y)1 =  6(25x5)(-y)1 = 6(32)x5(-y) = -192x5y\r\n" );
document.write( "C(6,4)(2x)4(-y)2 = 15(24x4)(-y)2 = 15(16)x4y2 = 240x4y2 \r\n" );
document.write( "C(6,3)(2x)3(-y)3 = 20(23x3)(-y)3 = 20(8)x3(-y3) = -160x3y3\r\n" );
document.write( "C(6,2)(2x)2(-y)4 = 15(22x2)(-y)4 = 15(4)x2y4 = 60x2y4 \r\n" );
document.write( "C(6,1)(2x)1(-y)5 =  6(21x1)(-y)5 = 6(2)x1(-y5) = -12xy5\r\n" );
document.write( "C(6,0)(2x)0(-y)6 =  1(20x0)(-y)6 = 1(1)x0y6 = 1(1)1y6 = y6\r\n" );
document.write( "\r\n" );
document.write( "Answer:\r\n" );
document.write( "\r\n" );
document.write( "(2x - y)6 = \r\n" );
document.write( "64x6 - 192x5y + 240x4y2 - 160x3y3 + 60x2y4 - 12xy5 + y6 \r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );