Question 128
Let $\mathbb{R}$ denote the set of real numbers. Determine all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
f(x) f(y) = x f(f(y-x)) + x f(2x) + f\left(x^{2}\right)
$$
holds for all real numbers $x$ and $y$.
$$
f(x) f(y) = x f(f(y-x)) + x f(2x) + f\left(x^{2}\right)
$$
holds for all real numbers $x$ and $y$.