Simplify:
$(a^{2} - b^{2}) (x^{2} - y^{2}) + 4 a b x y$

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Solution

Now,
$(a^{2} - b^{2}) (x^{2} - y^{2}) + 4 a b x y$
$= (a x)^{2} + (b y)^{2} + 2 a b x y - (a y)^{2} + 2 a b x y - (b x)^{2}$
$= {(a x)^{2} + (b y)^{2} + 2 a b x y} - {(a y)^{2} - 2 a b x y + (b x)^{2}}$
$= (a x + b y)^{2} - (a y - b x)^{2}$
$= (a x + b y + a y - b x) (a x + b y - a y + b x)$

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