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

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#### Solution

Let 2x - 3y = a, 4z - 2x = b, 3y - 4z = c

∴ a + b + c = 2x - 3y + 4z - 2x + 3y - 4z = c

∵ a + b + c = 0 ∴a^{3} + b^{3} + c^{3} = 3abc

∴ (2x - 3y)^{3} + (4z - 2x)^{3} + (3y - 4z )^{3} = 3(2x - 3y )(4z - 2x)(3y - 4z)

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