The Binomial Theorem in a Commutative Ring

In the setting of Commutative Rings, Fields and Ordered Fields: Standard Notation, let $R$, with $+$, $\cdot$, $0$ and $1$, be a commutative ring, let binomial coefficients $\binom{n}{k}$ be as in The Binomial Coefficient §binomial, and let $x,y\in R$ and $n\in\mathbb{N}_{0}$.

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