Theorem T61 (x+y)n=∑k=0n(nk)x(x−kz)k(y+kz)n−k(x + y)^n = \sum_{k=0}^n \binom{n}{k} x (x - k z)^k (y + k z)^{n - k} (x+y)n=k=0∑n(kn)x(x−kz)k(y+kz)n−k for integer n≥0n \geq 0n≥0 and x≠0x \neq 0x=0. notation-integer-finite-summation