finding the coefficient of $x^{14}$ in the expression: $\frac{5x^2-x^4}{(1-x)^3}$ I have a homework question which requires me to find the coefficient of $x^{14}$ in the expression: $\dfrac{5x^2-x^4}{(1-x)^3}$
I have not figured out a way to do this (I believe this is because my algebra is weak).
This is a question in a combinatorics class and has to do with Generating Functions if that is any help.
Help is greatly appreciated. Thanks, Jason

You are after:
\begin{align}
[x^{14}] \frac{5 x^2 - x^4}{(1 - x)^3}
  &= 5 [x^{12}] (1 - x)^{-3} - [x^{10}] (1 - x)^{-3} \\
  &= 5 (-1)^{12} \binom{-3}{12} - (-1)^{10} \binom{-3}{10} \\
  &= 5 \binom{12 + 3 - 1}{3 - 1} - \binom{10 + 3 - 1}{3 - 1} \\
  &= 389
\end{align}
Here I used:
$$
\binom{-n}{k} = (-1)^k \binom{k + n - 1}{n - 1}
$$
