What's this function called: $a^2 + b^2 + 2(ab)$? This is a formula for calculating the 2th power of a number, for example if you want to calculate the 2th power of 5:
$\begin{align*}
a&= 2\\
b&= 3
\end{align*}$
$ 5^2 = a^2 + b^2 + 2(ab)$
Sorry if that's not the right notation, but you'll get the point. Question is, what's the formula/method called?

As J. M. and lhf said, this is an example of a Binomial expansion. Other examples include $$(a+b)^1=a^1+b^1$$ $$(a+b)^2=a^2+2ab+b^2$$ $$(a+b)^3=a^3+3a^2b+3ab^2+b^3$$ $$(a+b)^4=a^4+4a^3b+6a^2b^2+4ab^3+b^4$$ and so on. The coefficient of the factor $a^m b^{n-m}$ in the expansion of $(a+b)^n$ is the number of ways of picking $m$ instances of $a$ out of $n$ possible instances of $a$ or $b$, which is the binomial coefficient $${n\choose m}=\frac{n!}{m!(n-m)!}.$$
