When

$\displaystyle a - \frac{1}{a} = 2$

then

$\displaystyle a^3 - 2a^2 - \frac{2}{a^2} - \frac{1}{a^3} = ? $

The answer is $\displaystyle 2$

I tried making a trinomial with $\displaystyle a - \frac{1}{a} = 2$ and I got $\displaystyle a^2 - 2a - 1$, but after this I wasn't able to solve for a.

What should I do to get to the result $\displaystyle 2$?

Thanks in advance.