real analysis - What can we conclude from $f(x+y)+f(x-y)=f(xy)$?

Let $f : \mathbb{R}\rightarrow\mathbb{R}$ be a function such that $f(x + y) + f(x − y) = f(xy)$ for all $x, y \in\mathbb{R}$. Then $f$ is:

A. Strictly increasing.

B. Strictly decreasing.

C. Identically zero.

D. Constant but not necessarily zero.

I have no idea how to do this. Thanks for any hint.