Algebra II: What Is the Binomial Theorem?

By Mary Jane Sterling

Part of Algebra II Workbook For Dummies Cheat Sheet

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 a0, which is really a 1. The powers on b increase from b0 until the last term, where it’s bn. Notice that the power of b matches k in the combination.