Binomial Expressions – Definition and Examples
Definition: Binomial expressions are polynomials that consist of two algebraic terms. You will need to find the greatest common factor in order to to factor binomial expressions.
Example: Binomial expressions may have a common factor, such as the variable a in the expression: ab + ac
Binomial Expressions – Greatest Common Factor Quiz
Choose the answer which has factored out the greatest common factor. You may wish to scroll down to see the further examples on this page before attempting the quiz below.
| [WpProQuiz 6] |
Types of Binomials – Further Examples
There are different types of binomial expressions.
Perhaps the most common types of binomial expressions are: factored quadratics, the difference of two perfect squares, the difference of two perfect cubes, the sum of two perfect cubes, and binomials that share a common factor.
Factored Quadratic
A factored quadratic consists of two binomials that are multiplied using the FOIL method.
A factored quadratic is in the following format:
(x ± n)(x ± n)
If you need help with this skill, please visit our post:
Difference of two perfect squares
The difference of two perfect squares consists of a binomial in the format:
a2 – b2
When the difference of two perfect squares is factored, it consists of two binomial expressions in the following format:
(a + b)(a – b)
If you need to review this skill, please see our post:
Factoring the difference of two perfect squares
Difference of two perfect cubes
The difference of two perfect cubes consists of a binomial in the format:
a3 – b3
When we factor the difference of two perfect cubes, the result is a binomial expression and a polynomial expression in this format:
(a – b)(a2 + ab + b2)
Sum of two perfect cubes
The sum of two perfect cubes consists of a binomial in the format:
a3 + b3
When we factor the sum of two perfect cubes, we have a binomial expression and a polynomial expression in this format:
(a + b)(a2 – ab + b2)
If you need to review how to factor the sum or difference of two perfect cubes, please see our post:
Factoring the sum or difference of two perfect cubes
Binomials that Share a Common Factor
Binomials that share a common factor are in the form:
ab + ac
To factor this type of binomial, we expand the expression and factor as show below.
ab + ac =
(a × b) + (a × c) =
a[(a × b) + (a × c)] =
a(b + c)
Polynomials – Further Exercises
If you found the previous problems difficult, you may want to try the following exercises:
Finding the Greatest Common Factor
