Question 160
Determine all polynomials $P \in \mathbb{R}[x, y]$ such that
$$
P(a, b^2 - ac) + P(b, c^2 - ab) + P(c, a^2 - bc) = 0
$$
for all $a, b, c \in \mathbb{R}$.
$$
P(a, b^2 - ac) + P(b, c^2 - ab) + P(c, a^2 - bc) = 0
$$
for all $a, b, c \in \mathbb{R}$.