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Monomial Calculator

Monomial Calculator

Enter a monomial expression and the tool will simplify it.


Enter the Expression:


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How easy was it to use our calculator? Did you face any problem, tell us!

Now you could make use of this free monomial calculator to solve monomials expressions within a couple of taps. Not only this, but the fast calculations done by this calculator will amaze you with accurate results.

What about moving ahead and discussing more about monomial algebra and how easy it is to simplify them either manually or by using this calculator.

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What Is a Monomial?

In algebraic terms:

“Monomial refers to an expression containing single term without any operator”

Monomials only contain a number or a variable. Also you can recall a number multiplied by variable as a monomial. But there is no chance to put more than one term in the expression. Also, the power of the monomials must be any whole number. This may introduce a little bit of difficulty for you to understand the concept. That is why we have developed this factor out a monomial calculator so as to get instant simplification of the single terms’ expressions.

You can not say that a monomial may be a polynomial. A polynomial is the expression that has two or more terms along with arithmetic operators in it. For instance, you may consider binomials and trinomials as polynomials. And when it comes to simplifying monomials, the free rational expression calculator is the only best choice for you.

Monomial Rules:

Before you start exploring monomials more, let it be clear you can not do so without keeping the following rules in your mind:

  • When you find product of a coupe of monomials, you will get a new monomial again
  • If you go by multiplying a monomial with a constant number, the output will again be a monomial
  • If a single algebraic term has negative or fractional exponent, then it can not be considered as monomial

Note: Keep in mind that numbers like 34, 24, 2323 are also considered monomials.

Monomial Parts:

In general, a monomial has three main parts that are described as follows as also determined by this degree of the monomial calculator.

Degree of Monomial:

The summation of all exponents raised to the variables involved in the expressions is known as the degree of the monomial.

For instance:

The monomial \(8x^{4}y^{2}\) is bearing the highest degree of 6 that you can verify by using this monomials calculator with work.

With the help of this online degree of monomial calculator, you can work for the highest power of the monomial sentence. And apart from this, we have another degree of polynomial calculator that also allows you to calculate the degree of any simple to complex polynomial in a matter of seconds.

Coefficient of Monomial:

When a whole number is multiplied by any variable, it is called a coefficient.

For instance:

In the following monomial:

\(5z^{3}\), the number 5 is known as the coefficient.

Literal Part of Monomial:

The part of the monomial containing variables and powers of indices is known as the literal part.

For instance:

In a monomial \(3x^{2}y^{4}\), the literal part is \(x^{2}y^{4}\)

Arithmetic Operations on Monomials:

Like simple numbers, we can also add monomials. And this can also be done swiftly by utilising our best monomials calculator. But if you are doing manual computations, then it is a must to undertake the following rules:

Addition of Monomials:

You can only add up like monomials.and if there are different ones, you will actually get a polynomial and not monomial. The generic expression for calculating addition of monomials is as follows:

$$ ax^{n} + bx^{n} = \left(a+b\right)x^{n} $$

Subtraction of Monomials:

Get going to subtract a couple or more monomials by using the formula below:

$$ ax^{n} – bx^{n} = \left(a-b\right)x^{n} $$

Multiplication of Monomials:

Here arise a couple of cases. So let’s go through these one by one:

Case # 01:

Monomial Product by Number:
This is the simplest multiplication of the monomials in which the number is multiplied by the coefficients of the monomial to produce the results. However, the online monomials calculator also lets you find the product of constant by these algebraic expressions in no time while maintaining accuracy in calculations.

Case # 02:

Product of one Monomial by Another:

Well this method of multiplication involves specific instruction for exponents as well. When you multiply the monomials the powers of identical variables are always added up. For instance, you can also determine a product by this free factor out a monomial calculator with exponents.

However, the generic equation is given below if you are interested to perform calculations manually:

$$ ax^{n} . bx^{m} = \left(a.b\right)\left(x^{n.m}\right) = \left(a.b\right)x^n+m $$

Division of Monomials:

Remember following key points if you are about to divide like monomials:

  • The degree of dividend must be greater or equal to the divisor monomial. If the process goes inverted, the result would be an algebraic expression
  • Also, the like variables will always be written with their exponents being subtracted. For ease, look at the equation as under:

$$ \frac{ax^{n}}{bx^{m}} = \frac{a}{b}x^n-m $$

How To Simplify Monomials?

No doubt simplifying monomials is not as easy as it is considered. But you people do not need to panic at all. As we will be resolving a few examples to clarify how you could understand the simplification technique of these simple but tricky algebraic expressions.

Example # 01:

How to find the degree of a monomial given below:

$$ 3xy + 2y\left(2x^{2}\right) $$


Simplifying monomial that is given:

$$ 3xy + 2y\left(2x^{2}\right) $$

$$ = 3xy + 4x^{2}y $$

$$ = 7x^{3}y^{2} $$

Example # 02:

Add the following monomials that are given as under:

$$ 2, 3y^{2}, 5x, 7x^{3}y $$


Here we have:

$$ = 2 + 3y^{2} + 5x + 7x^{3}y $$

As there are no like terms to be added, the final answer will be the same as given in the statement. For further verification, we advise you using this free adding monomial calculator.

How Monomial Calculator Works?

Let’s explore how you could utilise this free monomial solver by providing certain input expressions:


  • In the designated field, write down the monomial expressions
  • Now tap the calculate button


The free factor monomials calculator with work does the following calculations:

  • Simplify the monomials by applying various arithmetic operations on them


What is the meaning of monomial in mathematics?

Simply uttering, monomial is ust a taxonomic term used for the expression containing one quantity in it.

What makes a monomial linear?

A degree of monomial that is equal to 1 actually makes it linear mathematically.

Can a monomial be negative?

The coefficient of the monomial can be both negative or positive, even it can be zero. But when it comes to the exponents of the expressions, it can never be negative and is always positive.

Is every polynomial a monomial?

No, but every monomial can be considered a factor of polynomial.


Identifying monomials reduces the complexity while discussing polynomial expressions. And that is why this technique is quite effective while carrying out complicated algebraic calculations. And rest when it comes to secure and fastest collections, our best factor monomials calculator is the only choice you are left with for sure.


From the source of Wikipedia: Monomial, Monomial basis, Multi-index notation, Degree

From the source of Khan Academy: Multiply monomials, Symmetry of polynomials, Equations

From the source of Lumen Learning: Multiplying Monomials, Simplifying Expressions, Exponent Properties, Power Property