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Mathematics

Factorise the following:

64x3 + 1

Factorisation

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Answer

64x3 + 1 = (4x)3 + (1)3.

We know that,

a3 + b3 = (a + b)(a2 - ab + b2)

∴ (4x)3 + (1)3 = (4x + 1)[(4x)2 - 4x.1 + 12]

= (4x + 1)(16x2 - 4x + 1).

Hence, 64x3 + 1 = (4x + 1)(16x2 - 4x + 1).

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