Binomial expansion

1. Nov 14, 2007

sara_87

Apply the binomial expansion to : (1+x)^n and show that the coefiicient of x^n in the expansion of (1+x)^2n is:
(nC0)^2 +(nC1)^2 +...+(nCn)^2
hint: (nCm)=(nC(n-m))

my approach:

(1+x)^n = x^n + nx^(n-1) + (nC2)x^(n-2) +...+ 1

(1+x)^2n = x^(2n) + nx^(2n-1) +...+ x^n

i dont know what to do next. it looks easy but i cant figure it out.