Prove that

\[ (1-x^3)^n = (1-x)^{3n} + 3nx (1-x)^{3n-2} + \dfrac{3n(3n-3)}{2\times 1} x^2 (1-x)^{3n-4} + \cdots + 3^n x^n (1-x)^n . \]

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TopNewestR. H. S. Taking \((1-x)^n\) common, what remains is the Binomial expansion of \([3x + (1-x)^2]\) to the power n. Hence proved.

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