Theorema binomiale

Theorema explicatum per geometriam

Theorema binomiale seu binominale dicit:

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

ubi k coefficiens binomialis est.

Latius expressum:

$(x+y)^{n}={\binom {n}{0}}x^{n}+{\binom {n}{1}}x^{n-1}y+\ldots +{\binom {n}{n-1}}xy^{n-1}+{\binom {n}{n}}y^{n}=\sum _{k=0}^{n}{\binom {n}{k}}x^{n-k}y^{k}.$