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Factorize:(2x − 3y)3 + (4z − 2x)3 + (3y − 4z)3 |
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Answer» (2x − 3y)3 + (4z − 2x)3 + (3y − 4z)3 Let 2x – 3y = a , 4z – 2x = b , 3y – 4z = 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 (2x − 3y)3 + (4z − 2x)3 + (3y − 4z)3 = 3(2x − 3y)(4z − 2x)(3y − 4z). |
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