Monomial Calculator

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.

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.

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.