The Square and the Fourth Power of a Sum

In the setting of Commutative Rings, Fields and Ordered Fields: Standard Notation, let $R$, with $+$, $\cdot$, $0$ and $1$, be a commutative ring, and let $s,t\in R$.

¶ $(s+t)^{2}=s^{2}+2st+t^{2}$.

¶ $(s+t)^{4}=s^{4}+4s^{3}t+6s^{2}t^{2}+4st^{3}+t^{4}$.