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प्रश्न
Find : (a - b)(a - b)(a - b)
उत्तर
(a + b)(a + b)(a + b)
= (a × a + a × b + b × a + b × b)(a + b)
= (a2 + ab + ab + b2)(a + b)
= (a2 + b2 + 2ab)(a + b)
= a2 × a + a2 × b + b2 × a + b2 × b + 2ab × a + 2ab × b
= a3 + a2 b + ab2 + b3 + 2a2b + 2ab2
= a3 + b3 + 3a2b + 3ab2
replacing b by -b, we get
= a3 + (-b)3 + 3a2(-b) + 3a(-b)2
= a3 - b3 - 3a2b + 3ab2
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