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