Question 1
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 $x^{2} - 2 x y + y^{2}$ satisfies this condition). Given that $(x - y)$ is a factor of $P(x, y)$, show that $(x - y)^{2}$ is a factor of $P(x, y)$.