I need to find the derivative of $x^2(x+1)^n$.

I need to use Leibniz formula but I just can't get the result.
We are supposed to get this :
[![Correct Result](https://i.stack.imgur.com/4aTZX.png)](https://i.stack.imgur.com/4aTZX.png)

But I got nearly the same kind :
$$x^2n! + 2xn!(x+1) + 2\frac{n!}{2!}(x+1)^2$$
$$= n!(x^2 + 2x(x+1) + (x+1)^2 $$
[![My Work](https://i.stack.imgur.com/VOYOb.jpg)](https://i.stack.imgur.com/VOYOb.jpg)
It starts from the mess below the horizontal line.
So I don't know how to get the result. I really can't understand what I did wrong. I succeeded in similar questions like nth derivative of $(x-a)^n(x-b)^n$.
I would really appreciate it if someone could lend a hand.
Thank you in advance!