Factorise : $250 x^{3} - 432 y^{3}$

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Solution

We know that,
$a^{3} - b^{3} = (a - b) (a^{2} + b^{2} + a b)$

Now,
$250 x^{3} - 432 y^{3} = 2 (125 x^{3} - 216 y^{3})$

$= 2 {(5 x)^{3} - (6 y)^{3}}$

$= 2 (5 x - 6 y) (25 x^{2} + 36 y^{2} + 5 x \times 6 y)$

$= 2 (5 x - 6 y) (25 x^{2} + 36 y^{2} + 30 x y)$

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