functional equations - Find all functions $f:mathbb Rto mathbb R$ such that $f(a^2+b^2)=f(a^2-b^2)+f(2ab)$ for every real $a$,$b$

I guessed $f(a)=a^2$ and $f(a)=0$, but have no idea how to get to the solutions in a good way.

Edit: I did what was suggested:

from $a=b=0$

$f(0)=0$

The function is even, because from $b=-a$

$f(2a^2)=f(-2a^2)$.