For real numbers $a$ and $b$, define $a\textdollar b = (a - b)^2$. What is $(x - y)^2\textdollar(y - x)^2$?
$\left[ (x-y)^2 - (y-x)^2 \right]^2$ $\left[ (x-y)^2 - (x-y)^2 \right]^2$ $[0]^2$ $0 \Rightarrow $ $\fbox{0}$.