If , then x = (a + b + c), then (x – a)³ + (x – b)³ + (x – c)³ can be factorized as: 1. (x - a)(x - b)(x - c) 2. 3. 3(x - a)(x - b)(x - c) 4. none of these

Question

KnowledgeBoat · Accepted Answer

Given, Let, p = x - a, q = x - b, r = x - c Adding, ⇒ p + q + r = (x - a) + (x - b) + (x - c) ⇒ p + q + r = 3x - a - b - c ⇒ p + q + r = 3x - (a + b + c) ⇒ p + q + r = 3 - (a + b + c) ⇒ p + q + r = (a + b + c) - (a + b + c) ⇒ p + q + r = 0 If p + q + r = 0, we use identity, p3 + q3 + r3 = 3pqr ⇒ (x - a)3 + (x - b)3 + (x - c)3 = 3(x - a)(x - b)(x - c). Hence, option 3 is correct option.

Mathematics

If , then x = (a + b + c), then (x – a)³ + (x – b)³ + (x – c)³ can be factorized as: 1. (x - a)(x - b)(x - c) 2. 3. 3(x - a)(x - b)(x - c) 4. none of these

Factorisation

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If , then x = (a + b + c), then (x – a)³ + (x – b)³ + (x – c)³ can be factorized as: 1. (x - a)(x - b)(x - c) 2. 3. 3(x - a)(x - b)(x - c) 4. none of these

Factorisation

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