\[\left( x^{2} - y^{2} \right)^{2} =\]
\[= \left( x^{2} \right)^{2} - 2x^{2}y^{2} + \left( y^{2} \right)^{2} =\]
\[= x^{4} - 2x^{2}y^{2} + y^{4}.\ \]