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Mathematics

Factorise the following:

7a3 + 56b3

Factorisation

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Answer

7a3 + 56b3 = 7(a3 + 8b3)

= 7[(a)3 + (2b)3]

We know that,

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

∴ 7[(a)3 + (2b)3] = 7(a + 2b)[a2 - a.2b + (2b)2]

= 7(a + 2b)(a2 - 2ab + 4b2).

Hence, 7a3 + 56b3 = 7(a + 2b)(a2 - 2ab + 4b2).

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