# Combine Like Terms Calculator

Calculator to combine like terms in equations is a free online tool that allows you to simplify equations by combining like terms. STUDYQUERIES’s online tool is extremely helpful when solving polynomial equation problems, as it makes the calculations process quick and easy.

## Steps to Use the Combine Like Terms Calculator

Combining like terms with this tool is very simple. All you have to do is follow the instructions.

• Step 1: Input the complete equation in the first input box, which is across the “Enter Terms” field.
• Step 2: Click “Combine Like Terms”.
• Step 3: Clicking on “Combine Like Terms” will open a new window where all the like terms will be combined.

## What does Combine Like Terms mean?

Let’s take a quick look at an algebraic expression before discussing like and unlike terms. Mathematically, an algebraic expression is an expression made up of variables and constants, as well as additions and subtractions.

A variable in an expression is a term whose value is unknown, while a constant term has a known value. It is called a coefficient when there is a numerical number corresponding to the variable. Examples of algebraic expressions include

$$3x + 4y -7, 4x – 10, 2x^2 − 3xy + 5$$ etc.

We will learn the meaning of like terms and how to combine them in this article.

In algebraic expressions, terms are normally separated by addition or subtraction.

For instance, a monomial expression has only one term. For example, $$3x, 5y, 4x,$$ etc. Similarly, a binomial expression contains two terms, for instance, $$3x + y, 2x + 7, x + y$$ etc. Trinomials contain three terms, whereas polynomials of higher degrees contain many terms.

In Algebra, like terms are terms with identical variables and exponents, regardless of their coefficients. An algebraic expression combines like terms so that the result of the expression can be calculated easily.

For example, $$7xy + 6y + 6xy$$ is an algebraic equation whose terms are $$7xy$$ and $$6xy$$. Therefore, this expression can be simplified by combining like terms as $$7xy + 6xy + 6y = 13xy + y$$. When combining like terms, we add only the coefficients of the terms.

On the other hand, unlike terms are terms that do not have identical variables and exponents.

For example, an expression $$4x + 9y$$ contains terms because x and y are different and not raised to the same power.

### Key Terms

• Variables can represent a variety of numbers.
• A constant is a number that is not directly affected by a variable.
• Algebraic expressions are composed of numbers, variables, grouping symbols, and operation symbols. Each component of an algebraic expression, which is made up of several parts, is called a term.
• A numerical coefficient (or coefficient) represents the numerical part of a term. For example, in the term 5x, the numerical coefficient is 5. It means that the variable, x, is multiplied by 5.
• If there is no numerical coefficient associated with a term, we assume it has a coefficient of 1. For instance, x is the same as 1x, and -x is the same as -1x.

In this discussion, a “term” is a string of numbers that have been multiplied or divided together (remember that division is simply multiplication by the reciprocal). A term or terms are combined by addition or subtraction within the same expression. For instance, consider the expression:

$$(ax + bx)$$

This expression consists of two terms. It is interesting to note that both terms have an x in common. Therefore, the common factor variable can be eliminated, leading to

$$(a + b)x$$

If the expression in parentheses can be calculated, that is, if the variables in the expression in parentheses are known numbers, then the calculation can be written as a+b. This new number should be juxtaposed with the remaining unknown number. In expressions, terms that share a common, unknown factor (or multiple unknown factors) are called like terms.

To provide an example for the above, let a and b have numerical values, so that their sum may be calculated. For ease of calculation, let a=4 and b=3. The original expression becomes

$$= 4x+3x$$

Factors that may be considered

$$= (4+3)x$$

or, equally,

$$= 7x.$$

As a result, we can conclude

$$4x+3x = 7x$$

The known values for the unlike parts of two or more terms are called coefficients. In this example, we can see that when terms with the same coefficients appear in an expression, they can be combined by adding or subtracting (whichever is indicated by the expression) the coefficients and maintaining the common factor between both terms. A combination of like terms is called combining like terms, and it is useful for solving equations.

### How to Combine the Like Terms?

Combining like terms is the process of simplifying expressions by adding or subtracting variables and coefficients. When two terms have the same variable and exponent, they are said to be “like”. Below is an example of two different terms that are unlike:

$$4x^2 + 7$$

The terms cannot be added together because they are unlike. For example, if the expression were $$4x^2 + 7x^2,$$ the two terms would be considered like terms. In order to simplify the expression, the coefficients would be added together, and the variable and exponent would be kept the same:

$$4x^2 + 7x^2 = 11x^2$$

Combining like terms involves thinking of the variable as an object, and the coefficient as the number of objects. As an example, if Steve has 1 potato and 1 orange, he cannot combine them since they are not the same.

1 potato + 1 orange = 1 potato + 1 orange

However, if both objects he had were potatoes instead, they could be combined since they are like terms.

1 potato + 1 potato = 2 potatoes

Variables and exponents are like different types of food – we need to make sure they are the same before adding them together.

While the examples above have been relatively simple, equations and expressions can include many more terms and variables. To combine like terms, follow these steps:

• Consider the expression and determine if any of the terms are like terms: in order for terms to be considered like terms, both the variable and the exponent must be the same. In the absence of such terms, the expression is already simplified, and no terms can be combined.
• Similar terms should be grouped together. It is common practice to write terms in descending order according to their power.
• By adding, subtracting, etc., combine like terms.
• The ability to combine like terms is a fundamental aspect of algebra that allows us to solve algebraic equations. The following examples illustrate how to combine like terms in expressions and equations.

Let’s look at some examples to help us understand this concept.

Example: 1 Consider the expression: $$4x + y.$$

Due to the fact that x and y are different variables, this expression cannot be simplified.

Example: 2 To simplify an expression $$4x^2 + 3x + 4y + 8x + 9x^2$$

Solution: Collect and add the like terms which gives; $$9x^2 + 4x^2+ 8x + 3x + 4y => 13x^2 + 11x + 4y.$$

Based on this example, we can conclude that the terms have the same variables raised to the same exponent.

Example: 3 Simplify $$2xy + 4x^2 + 3yx +5y^2 +16x^2.$$

Solution: In this example, the terms 2xy and 3yx, as well as 4x² and 16 x² have identical variables. 2xy and 3yx are identical because of the commutative property of multiplication. Therefore, $$2xy + 3yx = 5xy$$ and $$4x^2 +16x^2 = 20 x^2.$$

Hence, $$2xy + 4x^2 + 3yx + 5y^2 + 16x^2 = 5xy + 20 x² + 5y^2$$

Example: 4 Simplify $$5m + 14m – 6n – 5n + 2m$$

Solution:  Rewrite the expression so that the like terms are next to each other.

$$5m + 14m – 6n – 5n + 2m$$

Combine the coefficients.

$$(5 + 14 + 2) m + (-6 + -5) n$$

$$21m – 11n$$

Example: 5 Simplify $$3x^2 + 3x – 4 – x^2 + x + 9$$

Solution: Sort the terms according to their degree;

$$= 3x^2 + 3x – 4 – x^2 + x + 9$$

$$= (3x^2 – x^2) + (3x + x) + (–4 + 9)$$

$$= (3 – 1) x^2 + (3 + 1) x + (5)$$

$$= (2) x^2 + (4) x + 5$$

$$= 2x^2 + 4x + 5$$

Example: 6 Simplify $$(10x^3 – 14x^2 + 3x – 4x^3 + 4x – 6)$$

Solution: Sort terms according to their degrees or exponentials;

$$= 12x^3 – 14x^2 + 3x – 4x^3 + 4x – 6$$

$$= (12x^3 – 4x^3) + (–14x^2) + (3x + 4x) – 6$$

$$= 8x^3 – 14x^2 + 7x – 6$$

Example: 7 Simplify $$[(6x – 8) – 2x] – [(12x – 7) – (4x – 5)]$$

Solution: Simplify from the inside out;

$$= [(6x – 8) – 2x] – [(12x – 7) – (4x – 5)]$$

$$= [6x – 8 – 2x] – [12x – 7 – 1(4x) – 1(–5)]$$

$$= [6x – 2x – 8] – [12x – 7 – 4x + 5]$$

$$= [4x – 8] – [12x – 4x – 7 + 5]$$

$$= 4x – 8 – [8x – 2]$$

$$= 4x – 8 – 1[8x] – 1[–2]$$

$$= 4x – 8 – 8x + 2$$

$$= 4x – 8x – 8 + 2$$

$$= –4x – 6$$

Example: 8 Simplify the expression $$–4y – [3x + (3y – 2x + {2y – 7}) – 4x + 5]$$

Solution: Begin simplifying from the innermost grouping;

$$= –4y – [3x + (3y – 2x + {2y – 7}) – 4x + 5]$$

$$= –4y – [3x + (3y – 2x + 2y – 7) – 4x + 5]$$

$$= –4y – [3x + (–2x + 3y + 2y – 7) – 4x + 5]$$

$$= –4y – [3x + (–2x + 5y – 7) – 4x + 5]$$

$$= –4y – [3x – 2x + 5y – 7 – 4x + 5]$$

$$= –4y – [3x – 2x – 4x + 5y – 7 + 5]$$

$$= –4y – [3x – 6x + 5y – 7 + 5]$$

$$= –4y – [–3x + 5y – 2]$$

$$= –4y – 1[–3x] – 1[+5y] – 1[–2]$$

$$= –4y + 3x – 5y + 2$$

$$= 3x – 4y – 5y + 2$$

$$= 3x – 9y + 2$$

Like Terms Distributive Property

These types of problems will be given to you and you’ll be asked to combine your like terms. Like terms are those that have the same variable multiplied by the same number. Therefore, 4x and 2x are the same as 3y and 5y. However, 4x and 3y are not the same thing, neither are 4x and 4y. This is because they share different variables.

The variables in two terms have to be the same for them to be like terms. In other words, if you had an x^2 term, another like term would also have an x^2 variable part. There would not be a like term if it had anything else, even if it was an x. The terms are separated by addition, subtraction, or division.

Combining like terms isn’t difficult in itself. The process involves adding or subtracting like terms as needed. If you are also dealing with parentheses and potentially the distributive property, then combining your like terms becomes more challenging. The distributive property tells you to multiply a term with all the other terms inside a pair of parentheses when it appears between parentheses.

If you follow these steps, you won’t have any problems.

• Step 1: Whenever you have parentheses, apply the distributive property. The first thing you need to do is apply the distributive property. Your parentheses will disappear once you have applied the distributive property. Looking at the problem 4x + x ( 3 – 2y ), you see a pair of parentheses with an x term in front of it. As a result, you need to apply the distributive property and multiply x with all the terms inside the parentheses. The result is as follows. You no longer have any parentheses.
• Step 2: Combine your terms. Since you’ve taken care of your parentheses, you can now combine your like terms. Remember to add or subtract only those terms that have exactly the same number and type of variable.

For your problem, $$4x + 3x – 2xy,$$ the only terms that are like terms are 4x and 3x. The -2xy is not a like term to any of the others. You can now add your 4x and 3x together to get 7x.

$$4x + 3x = 7x$$

Your answer then is $$7x – 2xy.$$ You have combined all the like terms that you could and you are done.

## Distribute And Combine Like Terms Calculator:

The term “Distribute and Combine Like Terms” refers to a mathematical process often used in algebraic expressions. It involves distributing a number or term to every term within parentheses, followed by combining the like terms. A calculator designed for this purpose would automate the steps involved in this process.

Example:
Consider the expression: 3(x + 2) – 2(x – 4)
To distribute and combine like terms, the calculator would perform the following steps:
Step 1: Distribute 3 to (x + 2) and distribute -2 to (x – 4):
3x + 6 – 2x + 8
Step 2: Combine the like terms by adding or subtracting coefficients of the same variables:
(3x – 2x) + (6 + 8)
x + 14

Solution using the calculator: By inputting the expression into the “Distribute and Combine Like Terms Calculator,” you would get the simplified result x + 14.

## Combine Like Terms Calculator With Steps:

A “Combine Like Terms Calculator with Steps” is a tool that helps users simplify algebraic expressions by combining like terms, providing a step-by-step breakdown of the process. It enables users to understand how each term is combined and simplifies the expression.

Example:
Consider the expression: 2x + 3y – x – 4y
The calculator with steps would perform the following breakdown:
Step 1: Combine like terms with the same variables:
(2x – x) + (3y – 4y)
x – y

Solution using the calculator: By inputting the expression into the “Combine Like Terms Calculator with Steps,” you would get the simplified result x – y, along with a detailed explanation of each step involved.

## Combine Like Terms Calculator Show Work:

A “Combine Like Terms Calculator Show Work” is a calculator that not only simplifies algebraic expressions by combining like terms but also displays the step-by-step work involved in the simplification process. It helps users understand and learn the process of combining like terms.

Example:
Consider the expression: 4x – 2 + 3x + 5
The calculator would perform the following steps to show work:
Step 1: Combine like terms with the same variables:
(4x + 3x) + (-2 + 5)
7x + 3

Solution using the calculator: By inputting the expression into the “Combine Like Terms Calculator Show Work,” you would get the simplified result 7x + 3, along with a detailed display of the work involved in each step.

## How To Combine Like Terms Calculator:

A “How to Combine Like Terms Calculator” refers to a tool that provides instructions and guidance on how to manually combine like terms in algebraic expressions. It assists users in understanding the process step-by-step, rather than automatically simplifying the expression.

Example:
Suppose you want to combine the like terms in the expression: 2x – 3 + 4x + 7
The calculator would provide the following instructions:
Step 1: Identify the terms with the same variables.
Step 2: Add or subtract the coefficients of the like terms.
(2x + 4x) + (-3 + 7)
6x + 4

Solution using the calculator: The “How to Combine Like Terms Calculator” would guide you through the process,

explaining each step, and provide the simplified result 6x + 4.

## Simplify The Expression By Combining Like Terms Calculator:

A “Simplify the Expression by Combining Like Terms Calculator” is a tool designed to simplify algebraic expressions by combining like terms automatically. It assists users by providing the simplified form of the expression without the need for manual calculations.

Example:
Consider the expression: 3x + 2 – 5x + 4
The calculator would perform the following steps to simplify the expression:
Step 1: Combine like terms with the same variables:
(3x – 5x) + (2 + 4)
-2x + 6

Solution using the calculator: By inputting the expression into the “Simplify the Expression by Combining Like Terms Calculator,” you would get the simplified result -2x + 6.

## Identify Terms And Coefficients Calculator:

An “Identify Terms and Coefficients Calculator” is a tool used to analyze algebraic expressions and identify the terms and coefficients within them. It assists users by breaking down the expression into its constituent parts.

Example:
Consider the expression: 4x + 2y – 3z
The calculator would identify the terms and coefficients as follows:
Terms: 4x, 2y, -3z
Coefficients: 4, 2, -3

Solution using the calculator: By inputting the expression into the “Identify Terms and Coefficients Calculator,” you would obtain the list of terms (4x, 2y, -3z) and coefficients (4, 2, -3) present in the expression.

## FAQs

How do you combine like terms?

A common technique for simplifying algebraic expressions. When combining like terms, such as 2x and 3x, we add their coefficients. For example,

$$2x+3x=(2+3)x=5x$$

What are 2 examples of like terms?

Terms whose variables (such as x or y) with any exponents (such as the 2 in x^2) are the same. Examples: 7x and 2x are like terms because they are both “x”.

Do you combine like terms first?

We begin by distributing the constant terms into the terms inside the parenthesis. Then, rearrange the terms so that similar terms are clustered together. Finally, combine like terms by adding or subtracting whichever is required.

Can you combine two different variables?

You can merge two or more variables to form a new variable. This is useful when you want to create a total awareness variable or when you want two or more categorical variables to be treated as one variable in your tables.

Are XY and YX like terms?

For XY and YX, the powers are the same i.e. 1. So, XY can be written as YX and vice versa. So, XY and YX can be classified as like terms.

What are the three terms in math?

Recall that a monomial is a single term, a binomial has two terms, a trinomial has three terms and a polynomial has many terms.

How do you find similar terms?

When we look at algebraic terms to find like terms, first we ignore the coefficients and only look if terms have the same variables with the same exponents. Those terms which qualify this condition are called like terms. All the given four terms are like terms because each of them has the same single variable ‘a’.

How To Combine Like Terms Calculator?

To use a “Combine Like Terms Calculator,” follow these steps:
Step 1: Enter the algebraic expression that you want to simplify.
Step 2: Click on the “Calculate” or “Simplify” button.
Step 3: The calculator will automatically combine the like terms in the expression and provide the simplified result.

Combine Like Terms What Is A Simpler Form Of Each Expression Calculator?

A “Combine Like Terms What Is a Simpler Form of Each Expression Calculator” is a tool that simplifies algebraic expressions by combining like terms and provides the simplified form of the expression as the output. It helps users determine the simplest possible form of an expression.

How Do You Combine Like Terms?

To combine like terms in an algebraic expression manually, follow these steps:
Step 1: Identify terms with the same variables. Like terms have the same variables raised to the same powers.
Step 2: Add or subtract the coefficients of the like terms. Keep the variables and their powers unchanged.
Step 3: Write down the combined terms as the simplified expression.

Example:
Consider the expression: 3x + 2y – 4x – y
Step 1: Like terms are 3x and -4x (both have the variable x) and 2y and -y (both have the variable y).
Step 2: Combine the coefficients of the like terms:
(3x – 4x) + (2y – y)
-x + y
Step 3: The simplified expression is -x + y.

How Do You Combine Like Terms On A Calculator?

To combine like terms using a calculator:
Step 1: Input the algebraic expression into the calculator.
Step 2: Use a “Combine Like Terms” or “Simplify” function on the calculator.
Step 3: The calculator will automatically combine the like terms and display the simplified form of the expression as the output.

What Is Expand And Combine Like Terms?

“Expand and Combine Like Terms” is a two-step process used to simplify algebraic expressions.
Step 1: Expand: Distribute any numbers or terms outside parentheses to every term inside the parentheses.
Step 2: Combine Like Terms: Combine the like terms by adding or subtracting the coefficients of the same variables.

Example:
Consider the expression: 2(x + 3) + 3(x – 2)
Step 1: Expand the expression:
2x + 6 + 3x – 6
Step 2: Combine like terms:
(2x + 3x) + (6 – 6)
5x

The result after expanding and combining like terms is 5x.

Are x^2 and x^3 Like Terms?

No, x^2 and x^3 are not like terms. Like terms have the same variables raised to the same powers. In this case, x^2 has the variable x raised to the power of 2, while x^3 has the variable x raised to the power of 3. Since the powers are different, x^2 and x^3 are not considered like terms.