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Algebraic Identities

Factorise: ...

Question

Factorise: $27 x^{3} - 8$

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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 $27 x^{3} - 8$ can be factorised as follows:

$27 x^{3} - 8 = (3 x)^{3} - (2)^{3} = (3 x - 2) [(3 x)^{2} + 2^{2} + (3 x \times 2)] = (3 x - 2) (9 x^{2} + 4 + 6 x)$

Hence, $27 x^{3} - 8 = (3 x - 2) (9 x^{2} + 4 + 6 x)$

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