CMO 1976 Problem 7

Let $P(x,y)$ be a polynomial in two variables $x,y$ such that $P(x,y)=P(y,x)$ for every $x,y$ (for example, the polynomial $x^2-2xy+y^2$ satisfies this condition). Given that $(x-y)$ is a factor of $P(x,y)$ , show that $(x-y)^2$ is a factor of $P(x,y)$ .