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Using the sum-of-cubes identity, $8 x^{3} + 27$ factorises as:

Class 9Algebraic IdentitiesPolynomials

A $(2 x + 3)^{3}$
B $(2 x + 3) (4 x^{2} - 6 x + 9)$
C $(8 x + 3) (x^{2} - 3 x + 9)$
D $(2 x + 3) (4 x^{2} + 6 x + 9)$

Step-by-Step Solution

a^{3} + b^{3} = (a + b) (a^{2} - ab + b^{2})

with

a = 2 x, b = 3 : (2 x + 3) (4 x^{2} - 6 x + 9)

.

Answer: B)

(2 x + 3) (4 x^{2} - 6 x + 9)

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