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Monomial Calculator

Enter a monomial expression and the tool will simplify it.

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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 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.

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:

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. 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: $$ 3xy + 2y\left(2x^{2}\right) $$ Solution: Simplifying monomial that is given: $$ 3xy + 2y\left(2x^{2}\right) $$ $$ = 3xy + 4x^{2}y $$ $$ = 7x^{3}y^{2} $$

How Monomial Calculator Works?

Let’s explore how you could utilise this free monomial solver by providing certain input expressions: Input:
  • In the designated field, write down the monomial expressions
  • Now tap the calculate button
Output: The free factor monomials calculator with work does the following calculations:
  • Simplify the monomials by applying various arithmetic operations on them


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.


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