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प्रश्न
Verify the following:
(a – b)(a – b)(a – b) = a3 – 3a2b + 3ab2 – b3
उत्तर
Taking L.H.S. = (a – b)(a – b)(a – b)
= (a – b)(a – b)2
= (a – b)(a2 – 2ab + b2) ...[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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