Finding the coefficient of a power series

Question

How would I find the coefficient of:

$[x^{10}]x^6(1-2x)^{-5}$

I know that I can simplify this as follows:

$[x^4](1-2x)^{-5}$

and that generally the following formula would be used to solve this:

$[x^n](1-x)^{-k}$ = $n+k-n \choose k-1$, but this can't be applied since there's a coefficient for the x-variable, $2x$.

Answer 1

One way to do this is to use the Newton generalized binomial theorem

$$ (1-2x)^{-5} = \sum_{k=0}^{\infty} {-5 \choose k }(-1)^k (2x)^k $$

which gives you

$$ [x^4](1-2x)^{-5} = (-1)^4 2^4{-5 \choose 4 }=1120. $$