The Expansion of the Square and the Fourth Power of a Sum of Real Numbers

In the setting of The Real Numbers: Standing Notation and Background, let $s,t\in\mathbb{R}$. Natural powers of a real number are those fixed in The Real Numbers: Standing Notation and Background §numbers, so that $s^{2}=ss$, $s^{3}=s^{2}s$ and $s^{4}=s^{3}s$ by claim 1 of Properties of Natural Number Powers in a Field, the natural numbers $2$, $3$ and $4$ being the successors of $1$, $2$ and $3$ respectively. Read in $\mathbb{R}$ through the canonical map, those natural numbers together with $6$ satisfy

by claims 1 and 4 of Properties of the Canonical Map from the Natural Numbers to an Ordered Field, and it is these real numbers that appear as coefficients below. Then the following hold.

1. (The square of a sum)¶

2. (The fourth power of a sum)¶