Factorise: $27 x^{3} + 1$ .

(3 x - 1) (9 x^{2} - 3 x + 1)

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(3 x + 1) (9 x^{2} - 3 x + 1)

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(3 x + 1) (9 x^{2} + 3 x + 1)

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(3 x - 1) (9 x^{2} + 3 x + 1)

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Solution

The correct option is B $(3 x + 1) (9 x^{2} - 3 x + 1)$
Using the identity:
$a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - a b)$
$27 x^{3} + 1 = (3 x)^{3} + 1^{3} = (3 x + 1) (9 x^{2} + 1 - 3 x)$

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