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Factorize:(3x − 2y)3 + (2y − 4z)3 + (4z − 3x)3 |
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Answer» (3x−2y)3 + (2y−4z)3 + (4z−3x)3 Let (3x−2y) = a, (2y−4z) = b , (4z−3x) = c a + b + c = 3x − 2y + 2y − 4z + 4z − 3x = 0 We know, a3 + b3 + c3 − 3abc = (a + b + c)(a2 + b2 + c2 − ab − bc − ca) ⇒ a3 + b3 + c3 −3abc = 0 or a3 + b3 + c3 = 3abc ⇒ (3x − 2y)3 + (2y − 4z)3 + (4z − 3x)3 = 3(3x − 2y)(2y − 4z)(4z − 3x) |
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