Question

Question #10746

Answer 1

`-1024`

Explanation:

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

`=(2-(1-x)^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^7`

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

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