Factorise the following:
$125 x^{3} + 64 y^{3} - 300 x^{2} y + 240 x y^{2}$

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Solution

$125 x^{3} - 64 y^{3} - 300 x^{2} y + 240 x y^{2}$
$= (5 x)^{3} - (4 y)^{3} - 3 (5 x) (4 y) [5 x - 4 y]$
$= (5 x - 4 y)^{3}$
$[∵ (a - b) = a^{3} - b^{3} - 3 a b (a - b)]$

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