A Monomial Calculator is a free online tool that displays a monomial of a given expression. STUDYQUERIES’S online monomials calculator tool makes the calculations faster and easier where it shows the monomial term in a fraction of seconds.

How to Use a Monomial Calculator?

The procedure to use a monomial calculator is as follows:

  • Step 1: Enter any expression in the input field
  • Step 2: Click the button “Simplify” to get the output
  • Step 3: The monomial term will be displayed in a new window

Monomial Calculator

Monomial And Monomial Calculator

In algebra, a monomial is an expression that has a single term, with variables and a coefficient. For example, 2xy is a monomial since it is a single term, has two variables, and one coefficient. Monomials are the building blocks of polynomials and are called ‘terms’ when they are a part of larger polynomials. In other words, each term in a polynomial is a monomial.

Monomial Calculator
Monomial Calculator

What is Monomial?

Monomial is defined as an expression that has a single non-zero term. It consists of different parts like the variable, the coefficient, and its degree. The variables in a monomial are the letters present in it. The coefficients are the numbers that are multiplied by the variables of the monomial. The degree of a monomial is the sum of the exponents of all the variables. Let us consider an expression \(6xy^2\). The variables, the coefficient, and the degree of this monomial are shown in the table given below. Observe the table to learn the various parts of the monomial \(6xy^2\).

  • The variables are the letters present in a monomial. Variables: x, y
  • The coefficient is the number that is multiplied by the variables. Coefficient: 6
  • The degree is the sum of the exponents of the variables in a monomial. The exponent of x is 1, and the exponent of y is 2, so the degree is 2 + 1 = 3. Degree: 3

How to Find a Monomial?

A monomial can be easily identified with the help of the following properties:

  • A monomial expression must have a single non-zero term.
  • The exponents of the variables must be non-negative integers.
  • There should not be any variable in the denominator.

Let us look at the following examples to identify monomials.

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 \(\times \) symbol stands for multiplication.

  • A monomial multiplied by a monomial is also a monomial.
    • \(2 \times 2 = 4 (a monomial)\)
    • \(2 \times x = 2x\)
    • \(2 \times 6 = 12\)
    • \(2 \times y = 2y\)
  • A monomial multiplied by a constant (number) is also a monomial.
    • \(-13 \times 7z = -91z\) (13 is the constant and 7z the monomial)
    • \((\frac{1}{8}) \times 8mn = -mn\) (⅛ is the constant and 8mn the monomial)
    • \((\frac{1}{5}) \times 5p = p\) (⅕ is the constant and 5p is the monomial)

Monomial Binomial Trinomial

If we observe the third example in the table given above, that is, \(3x^2 + y\), we see that it has 2 terms. An expression having two terms is called a binomial. Similarly, an expression having three terms is called a trinomial. For example, \(4x^2 + 2y + 6z\) is a trinomial. It is important to note that monomial, binomial, and trinomial are all types of polynomials. Look at the image given below to understand the difference between monomial, binomial, and trinomial.

Monomial Binomial Trinomial
Monomial Binomial Trinomial

Degree of a Monomial

The degree of a monomial is the sum of the exponents of all the variables. It is always a non-negative integer. For example, the degree of the monomial \(abc^2\) is 4. The exponent of the variable \(‘a’\) is 1, the exponent of variable \(‘b’\) is 1, the exponent of variable \(‘c’\) is 2. Adding all these exponents, we get, \(1 + 1 + 2 = 4\). Let us learn how to find the degree of a monomial with another example.

Example: Find the degree of the monomial: \(-4xy\).

In the given term, the coefficient is -4, and x and y are the variables. The exponent of the variable x is 1. The exponent of the variable y is 1. Therefore, the degree of the monomial is the sum of these exponents, that is, 1 + 1 = 2.

Factoring Monomials

While factoring monomial, we always factor coefficient and variables separately. Factorizing a monomial is as simple as factorizing a whole number. Consider the number 24. Let us see the factors of this number. The number 24 can be split into its factors as shown in the following factor tree:

factor a monomial

In the same manner, we can factorize a monomial. We just need to remember that we always factorize the coefficient and the variables separately.

Example: Factorize the monomial, \(15y^3\).

In the given monomial, \(15\) is the coefficient, and \(y^3\) is the variable.

The prime factors of the coefficient,15, are 3 and 5.

The variable \(y^3\) can be factored in as \(y × y × y\).

Therefore, the complete factorization of the monomial is \(15y^3 = 3 × 5 × y × y × y\).

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

Tips and Tricks on Monomials

Observe the following points which help in understanding the results of the arithmetic operations on a monomial.

  • A single term expression in which the exponent is negative or has a variable in it is not a monomial.
  • The product of two monomials is always a monomial.
  • The sum or difference of two monomials might not be a monomial.

FAQs

What is a monomial example?

Monomial is an expression that has a single non-zero term. Monomials can be numbers, variables, or numbers multiplied with variables. For example, 2, ab, and 42xy are examples of a monomial. A few other examples of monomials are 5x, 2y3, 7xy, x5.

What is a monomial simple definition?

  • a mathematical expression consisting of a single term.
  • a taxonomic name consisting of a single word or term.

What is a monomial and binomial?

monomial—A polynomial with exactly one term. binomial— A polynomial with exactly two terms. trinomial—A polynomial with exactly three terms. Notice the roots: poly– means many.

How do you know if it is a monomial?

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.