Find all solutions to the equation $f(x+y)+f(x-y)=2x^2-2y^2$ 
Find all solutions to the equation $f(x+y)+f(x-y)=2x^2-2y^2$

What's the best strategy here? 
I've tried substituting in values but I didn't get anything (if it was $2x^2+2y^2$ I could just substitute $y=0$ but the minus sign complicates the story).
The only other method  I know is isolation,but I don't think it's useful here.
Can you guys give me some hint ?
Edit:
The function in question looks similiar to some trig identity maybe ?

It would seem that there is, in fact, no solution. If we analyze two separate cases, we have:


*

*Setting $y = 0$ gives $f(x) = x^2$ for all $x$

*Setting $x = y$ gives $f(2x) = 0$ for all $x$
These two conditions are contradictory. 
