Theorema binomiale
Theorema binomiale seu binominale dicit: ( x + y ) n = ∑ k = 0 n ( n k ) x n − k y k ( 1 ) {\displaystyle (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 = ( n 0 ) x n + ( n 1 ) x n − 1 y + … + ( n n − 1 ) x y n − 1 + ( n n ) y n = ∑ k = 0 n ( n k ) x n − k y k . {\displaystyle (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}.}