Theorema binomiale

Theorema binomiale seu binominale dicit:

$(x+y)^n = \sum_{k=0}^{n}\binom{n}{k} x^{n-k}y^{k} \quad (1)$

Latius expressum:

$(x+y)^n = \binom n0 x^n + \binom n1 x^{n-1} y + \ldots + \binom n{n-1} x y^{n-1} + \binom nn y^n = \sum_{k=0}^n \binom n k x^{n-k} y^{k}.$