$(a+b)^2=a^2+2ab+b^2$
$(a-b)^2=a^2-2ab+b^2$
What are these two called in English? Are they called anything at all? I looked around on some math websites and Wikipedia, but I didn't find these rules. I did find the conjugate rule for the difference of two squares. That was useful, and I have now memorized that name, but that was not exactly what I was looking for.
Maybe they are not considered to be noteworthy rules so they have not been given a name in the English speaking world?
Update:
These are called "kvadreringsregler" in Swedish. I have found some translations to other languages, but not to English.
- Danish: Kvadratsætningen
- Swedish: Kvadreringsreglerna
- Norwegian: Kvadratsetningene
- Polish: Wzory skróconego mnożenia
- French: Identité remarquable
- English: ???
The proposed "binomial theorem" is called "binomialsatsen" in Swedish. This is considered to be a more generalized form of "kvadreringsregelerna". The French name for this literally translates into "remarkable identities". That gave me some interesting web search results.
We call remarkable identities to [sic] some binomial products that appear
very often in calculations with algebraic expressions.
Source: Mathspadilla
Could this be it?
Best Answer
I call both those identities binomial squares in my classes.