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

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Solution

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

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