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

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Solution

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

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