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Question
Factorize: a (a + b)3 - 3a2b (a + b)
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Solution
Taking (a + b) common in two terms
= (a + b){a (a + b)2 - 3a2b}
Now, using (a + b)2 = a2 + b2 + 2ab
= (a + b){a (a2 + b2 + 2ab) - 3a2b}
= (a + b){a3 + ab2 + 2a2b - 3a2b}
= (a + b){a3 + ab2 - a2b}
= (a + b) a{a2 + b2 - ab}
= a (a + b)(a2 + b2 - ab)
∴ a (a + b)3 - 3a2b (a + b) = a (a + b)(a2 + b2 - ab)
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