Factorize: $81 x^{3} - x y^{2}$

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Solution

We need to factorise the given expression.
$81 x^{3} - x y^{2}$
$= x (81 x^{2} - y^{2})$ (taking $x$ common)
$= x [(9 x)^{2} - (y)^{2}]$
(converting in the form $a^{2} - b^{2}$ )
$= x [(9 x - y) (9 x + y)] = x (9 x - y) (9 x + y)$

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