Why call it the Binomial Theorem?

Taking Statistics for Economists, and the book refers to the binomial theorem using as:

$\displaystyle (a + b)^n$ where n is # of Bernoulli trials.

I just realized though, although this is considering p(success) and p(failure) as the variables, since outcome space is also a variable, would not a more appropriate moniker be trinomial theorem? I do not know if this qualifies as a question or not, just looking for some clarification on the terminology since number of trials can be potentially infinite.