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

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Solution

$f (x) = a b (x^{2} + y^{2}) - x y (a^{2} + b^{2})$

$f (x) = a b . x^{2} - x (a^{2} y + b^{2} y) + a b y^{2}$

$f (x) = a x (b x - a y) - b y (b x - a y)$

$f (x) = (a x - b y) (b x - a y)$ .

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