Definition and Examples of Binomials in Algebra

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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) 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.

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Russell, Deb. "Definition and Examples of Binomials in Algebra." ThoughtCo, Apr. 2, 2021, Russell, Deb. (2021, April 2). Definition and Examples of Binomials in Algebra. Retrieved from Russell, Deb. "Definition and Examples of Binomials in Algebra." ThoughtCo. (accessed June 6, 2023).