# Algebra II: What Is the Binomial Theorem?

A *binomial* is a mathematical expression that has two terms. In algebra, people frequently raise binomials to powers to complete computations. The binomial theorem says that if *a* and *b* are real numbers and *n* is a positive integer, then

You can see the rule here, in the second line, in terms of the coefficients that are created using combinations. The powers on *a* start with *n* and decrease until the power is zero in the last term. That’s why you don’t see an *a* in the last term — it’s *a*^{0}, which is really a 1. The powers on *b* increase from *b*^{0 }until the last term, where it’s *b** ^{n}*. Notice that the power of

*b*matches

*k*in the combination.