Definition and Examples of Binomials in Algebra

A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial. Binomials are used in algebra. Polynomials with one term will be called a monomial and could look like 7x. A polynomial with two terms is called a binomial; it could look like 3x + 9. It is easy to remember binomials as bi means 2 and a binomial will have 2 terms.

A classic example is the following: 3x + 4 is a binomial and is also a polynomial,  2a(a+b) ² is also a binomial (a and b are the binomial factors).

The above are both binomials.

When multiplying binomials, you'll come across a term called the FOIL method which is often just the method used to multiply binomials. 

For instance, to find the product of 2 binomials, you'll add the products of the First terms, the Outer terms, the Inner terms, and the Last terms.

When you're asked to square a binomial, it simply means to multiply it by itself. The square of a binomial will be a trinomial. The product of two binomials will be a trinomial.

Example of Multiplying Binomials

(5 + 4x) x (3 + 2x)
(5 + 4x)(3 + 2x)
= (5)(3) + (5)(2x) + (4x)(3) + (4x)(2x)
= 15 + 10x + 12x + 8x²
= 15 + 22x + 8x²

Once you begin taking algebra in school, you'll be doing a great many computations that require binomials and polynomials.