Factorize $(3 x - 2 y)^{3} + (2 y - 4 z)^{3} + (4 z - 3 x)^{3}$

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Solution

$(3 x - 2 y)^{3} + (2 y - 4 z)^{3} + (4 z - 3 x)^{3} ∵ 3 x - 2 y + 2 y - 4 z + 4 z - 3 x = 0 ∴ (3 x - 2 y)^{3} + (2 y - 4 z)^{3} + (4 z - 3 x)^{3} = 3 (3 x - 2 y) (2 y - 4 z) (4 z - 3 x) {∵ x^{3} + y^{3} + z^{3} = 3 x y z i f x + y + z = 0}$

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