Question 90 (xi)

Factorise the following, using the identity, $a^{2} - 2 a b + b^{2} = (a - b)^{2}$ .

$a^{2} y^{3} - 2 a b y^{2} + b^{2} y$

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Solution

We have,
$a^{2} y^{3} - 2 a b y^{2} + b^{2} y = y (a^{2} y^{2} - 2 a b y + b^{2}) = y [(a y)^{2} - 2. a y . b + b^{2}] = y (a y - b)^{2} = y (a y - b) (a y - b)$

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