$\begin{align} & {{\left( x+y \right)}^{2}}-{{\left( x-y \right)}^{2}}=\left( x+y \right)\left( x+y \right)-\left( x-y \right)\left( x-y \right)= \\ & {{x}^{2}}+2xy+{{y}^{2}}-{{x}^{2}}+2xy-{{y}^{2}}=4xy=0\to xy=0 \\ \end{align}$