Factorize each of the following expressions :

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

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Solution

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

$∴ x^{2} + y - x y - x$
$= x^{2} - x y + y - x$
$= x (x - y) - 1 (- y + x)$
$= x (x - y) - 1 (x - y)$
$= (x - y) (x - 1)$

Hence, $x^{2} + y - x y - x = (x - y) (x - 1)$

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