Using elementary taylor series for taylor polynomial

Ok, so the problem is to use a sixth-degree Taylor polynomial centered at c for the function f to obtain the required approximation. Here's the info:

Function: $\displaystyle f(x)=x^2e^{-x}$

Center: $\displaystyle c=0$

Approximation: $\displaystyle f(1/4)$

Now, my main question is since there is an elementary Taylor series for $\displaystyle e^x$, which with a center at 0 is $\displaystyle \frac{e^x x^n}{n!}$, then the Taylor series for $\displaystyle e^{-x}$ must be $\displaystyle \frac{e^{-x} -x^n}{n!}$. So for $\displaystyle x^2e^{-x}$, could it be as simple as placing $\displaystyle x^2$ in front of the Taylor series for $\displaystyle e^{-x}$ since n is the value that is changing, so any term with only x can be treated as a constant?