Binomial

High School

Definition

A polynomial that is made up of two terms. It is an algebraic expression that is made up of the sum or differences of two seperate terms. Therefore, each of the seperate terms can be seen as monomials when they are alone. An example of this would be 2x + y.

Worked examples

\(3x + 5\)

Two terms — a variable term and a constant — joined by addition make a binomial.

\(7a^2 - 2b\)

Each term can have different variables and exponents; the key is exactly two terms.

Common mistakes

\(2x + 3y - 1\) is a binomial → \(2x + 3y - 1\) is a trinomial (three terms) Count the terms separated by + or − signs; a binomial has exactly two.
\(5xy\) is a binomial because it has two variables → \(5xy\) is a monomial (one term) The number of terms matters, not the number of variables; 5xy is a single product.
\((x + 2)(x - 3)\) is a binomial → \((x + 2)(x - 3)\) is a product of two binomials, but expands to a trinomial A binomial is a sum or difference of two terms, not a factored product.

Where you'll use it next

Binomials are central to factoring, multiplying polynomials (including FOIL), the binomial theorem, and solving quadratic equations in algebra and beyond.

Found in 1 StudyPug lesson

Understanding Polynomial Components: A Comprehensive Guide

Grade 10 Math

Dive into the world of polynomials! Learn to identify terms, coefficients, and degrees. Master standard form and leading terms. Boost your algebra skills with our in-depth guide to polynomial components.

10th Grade10th