Mathematics
Factorise:
250(a - b)3 + 2
Factorisation
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Answer
Given,
⇒ 250(a - b)3 + 2
⇒ 2[125(a - b)3 + 1]
⇒ 2{[5(a - b)]3 + (1)3}
By using the identity,
(a3 + b3) = (a + b)(a2 - ab + b2)
⇒ 2[5(a - b) + 1] {[5(a - b)]2 - 5(a - b) × 1 + (1)2}
⇒ 2[(5a - 5b + 1)(25(a - b)2 - 5(a - b) + 1)]
⇒ 2[(5a - 5b + 1)(25(a2 - 2ab + b2) - 5a + 5b + 1)]
⇒ 2[(5a - 5b + 1)(25a2 - 50ab + 25b2 - 5a + 5b + 1)]
Hence, 250(a - b)3 + 2 = 2[(5a - 5b + 1)(25a2 - 50ab + 25b2 - 5a + 5b + 1)].
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