Factorise :

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

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Solution

$a b (x^{2} + y^{2}) - x y (a^{2} + b^{2}) = a b x^{2} + a b y^{2} + x y a^{2} - x y b^{2} = a b x^{2} - x y a^{2} - x y b^{2} + a b y^{2} = a x (b x - a y) - b y (b x - a y) = (b x - a y) (a x - b y) A n s .$

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