Factorise: a3 + 3a2b + 3ab2 + b3 - 8 - Vidyadip

Question

Factorise:
a³ + 3a²b + 3ab² + b³ - 8

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Answer

a³ + 3a²b + 3ab² + b³ - 8
= (a + b)³ - 2³
=[(a + b) - 2][(a + b)² + (a + b)2 + 2²]
=(a + b - 2)[(a + b)² + 2(a + b) + 4]

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