Binomial theroem

Can anyone explain me this step please-

coefficient of xⁿ in [C₀(1+x)²ⁿ - C₁(1+x)^2n-2 + C₂(1+x)^2n-4............... ]
= coefficient of xⁿ in [-1 + (1+x)²]ⁿ

Thanks alot

2 Answers

The basic funda is that the expression [C0(1+x)2n - C1(1+x)2n-2 + C2(1+x)2n-4............... ] is the binomial expansion of [-1 + (1+x)2]ⁿ

So there should not be a lot to understand except the observation that (x+y)ⁿ=Sum(nCR. x^r)

Sometimes small things become a big trouble. Thanks alot sir!

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