Hello i'm new, i study Econometrics and i have some questions.

I am studying for my exams, and i had several exercises about computing the nth derivative. I totally don't know how to solve it (the last step).
Let n be given in neutral numbers (dunno how to type it correctly).
Let $\displaystyle F(x) = x^2(1+x)^n$ and write $\displaystyle F^{n}$ for the $\displaystyle n^{th}$ derivative of the function F. Compute $\displaystyle F^{n} $ by applying the Binomial Theorem to $\displaystyle (1+x)^n$

I finished until the part that i had the Binomial theorem worked out. But then the last step i totally don't get.

It has to be something with factorial this and factorial that...

Some other exercises would be:
$\displaystyle x^{3}(1+x)^{n}$ or calculate the $\displaystyle N+3^{th}$ derivative of F. $\displaystyle F(x)= 5x^{4}(1+x)^{N}$