Examples of Monomials

A monomial is an expression in algebra that contains one term, like 3xy. Monomials include numbers, variables or multiple numbers and/or variables that are multiplied together. Any number all by itself is a monomial, like 5 or 2,700. A monomial can also be a variable, like "b" or "y." It can also be a combination of these, like 98b or xy. Explore the rules of monomials, monomial degrees and monomial examples.

monomial examples monomial examples
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Monomial Definition

One of the first math terms you learn in algebra is monomials. When it comes to understanding the definition of a monomial, it’s pretty easy. Mono means “one.” So, monomial functions are those expressions that only have the one term. While a monomial can be a single number, variable or combination of a number and variables, it can’t be a negative exponent. Therefore, monomials have two rules.

The Rules of Monomials

Math always includes a few rules and monomials aren’t any different. There are two rules to remember about monomials. In these examples, the * symbol stands for multiplication.

1. A monomial multiplied by a monomial is also a monomial.

2 * 2 = 4 (a monomial)
2 * x = 2x
2 * 6 = 12
2 * y = 2y

2. A monomial multiplied by a constant (number) is also a monomial.

-13 * 7z = -91z (13 is the constant and 7z the monomial)
(⅛) * 8mn = -mn (⅛ is the constant and 8mn the monomial)
(⅕) * 5p = p (⅕ is the constant and 5p is the monomial)

Examples: Numbers That Are Monomials

Now, it's time to really look at a few examples of monomials. Monomials are positive numbers. It doesn't matter how big they are, they are still a monomial. See a few examples of monomial numbers in action.

  • 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
  • 100
  • 500
  • 1,000
  • 5,000
  • 10,000
  • 3,598,772
  • 4,000,000
  • 14,000,000
  • 14,100,300
  • 20,000,000

Examples: Variables That Are Monomials

It might be hard to think of a variable as a monomial, especially when you get to a group like abc. But remember one of the rules of monomials, a monomial multiplied by a monomial is still, you guessed it, a monomial. Therefore, variables multiplied by each other are also monomials. Look at a few examples.

  • x
  • y
  • xy
  • abc
  • mx
  • n
  • b
  • w
  • l
  • s
  • bxy
  • a
  • ax

Examples: Combinations of Numbers and Variables That Are Monomials

Numbers and variables aren't going to stand alone when it comes to monomials. They can work together. Therefore, 645a is still a monomial. Explore a few other examples of combinations of monomials.

  • 1x
  • 2y²
  • 32x³y
  • 653abc
  • 2g7g9g

Degrees of a Monomial Function

You might have noticed in the combinations that some monomials have an exponent. For example, 2y² has an exponent of 2. It also has a degree of 2. In a monomial, you can add the exponents of the variables together to find the degree of a monomial function. The exponent for a constant is always 0, and the exponent for a variable that doesn't have an exponent listed is always 1. For example:

5ab3c4
5, exponent = 0
a, exponent = 1
b, exponent = 3
c, exponent = 4
The total degree of this equation is 0 + 1 + 3 + 4 = 8
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What Is Not a Monomial

A monomial is an algebraic expression with only one term, so 132y÷ 9y or 47z + 2y are not monomials. These are called polynomials since they have a finite number of terms. Explore a few examples of equations that are not monomials.

  • 9a2 + 45a - 2
  • 8x5 + 21x3 - 9x
  • 8a - 15
monomial binomial trinomial example
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Understanding Monomials

All algebraic expressions with one term are examples of monomials — so there are countless examples that encompass the entire number system. Ready to keep your math knowledge going? Take a look at polynomials and monomials.