Elementary "binomial theorem" in English

Question

In German schools, the identitiy $(a+b)^2 = a^2 + 2ab + b^2$ is called the first binomial formula (literally translated). However, it seems to me this English term only refers to the more general binomial theorem which involves the former as a special case, but is much more powerful and complex, or to formulas involving the binomial.

Is there special terminology taught in schools for this kind of formula? What would be the best way to describe the process of creating a square (similar to completing the square) as in $x^2 + 2x + 1 = (x+1)^2$?

Answer 1

I might say of the folowing

• the simplest case of the binomial theorem.
• binomial theorem where the exponent is 2.
• binomial theorem where n = 2

Answer 2

You want to start with $4x^2+4x+1$ and come up with $(2x+1)^2$ ... for that I might say $4x^2+4x+1$ is a perfect square.

Answer 3

In my experience the usual school terminology treats it simply as a special case of factor(is)ing, alongside the distributive law, $a^2-b^2=(a+b)(a-b)$ and sometimes

$$a^3\pm b^3=(a\pm b)(a^2\mp ab+b^2)\;.$$

I’ve seen it called square of a binomial, but this name doesn’t seem to be as widespread as difference of (two) squares or even difference/sum of (two) cubes.