What is a simple proof of this differentiation property?

[td21]

$$
\frac{d^{2n}}{dx^{2n}}\left(x^2-1\right)^n = (2n)!
$$

 

[jedishrfu]

Try using an induction proof:

Step 1 prove for n=1

Step 2 Assume its true for k and the prove its true for k+1