Factorize each of the following expressions:

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

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Solution

Given: $x a^{2} + x b^{2} - y a^{2} - y b^{2}$

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

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

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