Question #10746

1 Answer
Dec 25, 2016

-10241024

Explanation:

(1+2x-x^2)^4(1+2xx2)4

=(2-(1-x)^2)^4=(2(1x)2)4

= terms that do not contribute to the coefficient of #x^7

  • the last term ((2-x)^2)^4#, using binomial expansion

So, the coefficient of x^7x7

= the coefficient in the expansion of ((2-x)^2)^4)=(2-x)^8((2x)2)4)=(2x)8

=-8C_7 2^7=8 X 128=1024=8C727=8X128=1024, using binomial expansion