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Binomial proof

Prove that

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

Note by Abdelfatah Teamah
8 months, 1 week ago

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

- 7 months, 4 weeks ago