Question 88 (xvi)

Factorise the following expression.

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

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Solution

We have, $(a x^{2} y - b x y z - a x^{2} z + b x y^{2}$
$= x (a x y - b y z - a x z + b y^{2})$
$= x (a x y - a x z - b y z + b y^{2})$
$= x [a x (y - z) + b y (- z + y)]$
$= x [(a x + b y) (y - z)]$

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

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