need to multiply
(x^2-1)^4
I get
-20x^9+32x^7-12x^5
Then i need to differentiate this 4 times
d^4/dx^4 (-20x^9+32x^7-12x^5)
I get
-10080x^6+6720x^4-720x^2
Is this right?
Think about this. Your highest power in the expansion will be $\displaystyle (x^2)^4 = x^8$. So you can't be right.
By the binomial theorem:
$\displaystyle (a + b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4$
You have $\displaystyle a = x^2$ and $\displaystyle b = -1$:
Thus
$\displaystyle (x^2 - 1)^4 = x^8 - 4x^6 + 6x^4 - 4x^2 + 1$
(I'd recommend making sure you know how to do it the long way as well. It's good practice.)
And make sure you take 4 derivatives. You only took 3.
-Dan