Factorise: $x^{3} + 8 y^{3}$

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Solution

We know the identity $a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$

Using the above identity, the equation $x^{3} + 8 y^{3}$ can be factorised as follows:

$x^{3} + 8 y^{3} = (x)^{3} + (2 y)^{3} = (x + 2 y) [(x)^{2} + (2 y)^{2} - (x \times 2 y)] = (x + 2 y) (x^{2} + 4 y^{2} - 2 x y)$

Hence, $x^{3} + 8 y^{3} = (x + 2 y) (x^{2} + 4 y^{2} - 2 x y)$

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