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Question

Factorise:
a3+3a2b+3ab2+2b3

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Solution

We have,
a3+3a2b+3ab2+2b3
=a3+b3+3ab(a+b)+b3
=(a+b)3+b3
=(a+b+b)((a+b)2+b2b(a+b)) [Using x3+y3=x+y(x2+xy+y2)]
=(a+2b)(a2+b2+2ab+b2abb2)
=(a+2b)(a2+ab+b2)

Hence, this is the answer.

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