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Question
Verify the following:
(a + b)(a + b)(a + b) = a3 + 3a2b + 3ab2 + b3
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Solution
Taking L.H.S. = (a + b)(a + b)(a + b)
= (a + b)(a + b)2
= (a + b)(a2 + b2 + 2ab) ...[Using the identity, (a + b)2 = a2 + 2ab + b2]
= a(a2 + 2ab + b2) + b(a2 + 2ab + b2)
= a3 + 2a2b + ab2 + ba2 + 2ab2 + b3
= a3 + 3a2b + 3ab2 + b3 ...[Adding like terms]
= R.H.S.
Hence verified.
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