Factorise: $8 x^{3} - {(2 x - y)}^{3}$

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Solution

$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$
by using this ;
$8 x^{3} - (2 x - y)^{3} = (2 x)^{3} + (y - 2 x)^{3} = (2 x + y - 2 x)^{3} - 3 (2 x (y - 2 x)) (2 x + y - 2 x)$
$= y^{3} - 6 x y (y - 2 x) = y (y^{2} - 6 x (y - 2 x))$

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