Factorize $(a - 3 b)^{3} + (3 b - c)^{3} + (c - a)^{3}$

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Solution

$(a - 3 b)^{3} + (3 b - c)^{3} + (c - a)^{3} ∵ a - 3 b + 3 b - c + c - a = 0 ∴ (a - 3 b)^{3} + (3 b - c)^{3} + (c - a)^{3} = 3 (a - 3 b) (3 b - c) (c - a) {∵ a^{3} + b^{3} + c^{3} = 3 a b c i f a + b + c = 0}$

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