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).
Example:
Let n be given in neutral numbers (dunno how to type it correctly).
Let F(x) = x^2(1+x)^n and write F^{n} for the n^{th} derivative of the function F. Compute F^{n} by applying the Binomial Theorem to (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:
x^{3}(1+x)^{n} or calculate the N+3^{th} derivative of F. F(x)= 5x^{4}(1+x)^{N}