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Question
Factorize the following expressions:
a3 + 3a2b + 3ab2 + b3 - 8
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Solution
= (a + b)3 - 8 [∵ a3 + 3a2b + 3ab2 + b3 = (a + b)3]
= (a + b)3 - 23
= (a + b - 2)((a + b)2 + (a + b)2 + 22)
= (a + b - 2)(a2 + b2 + 2ab + 2a + 2b + 4)
∴ a3 + 3a2b + 3ab2 + b3 - 8 = (a + b - 2)(a2 + b2 + 2ab + 2a + 2b + 4)
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