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Home>Math Worksheets > Algebra Worksheets > **Combining Like Terms**

Your students will use this collection of activity worksheets to learn how to solve for variables to simplify algebraic expressions. These sets of worksheets introduce your students to the concept of combining like terms, and provide examples, short practice sets, longer sets of questions, and quizzes. This is a paramount skill in algebra, you will need to master it in order to have an easy transition to higher level math. To combine like terms we either subtract or add numerical coefficients. You basically are cleaning up an expression or equation to just make it more workable. We suggest whenever you are evaluating expressions or equations to think about like terms first. This series of lessons and worksheets teach the steps for simplifying equations by matching or combining terms that are alike until there are no more steps that can be performed. A variety of equations are provided ranging from simple to advanced.

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## Combining Like Terms (Difficult) Lesson

Follow along and simplify this expression: x^{2} + 3x^{2} + 6x^{2} + 8x^{2}

## Difficult Worksheet 1

Simplify for each set of terms. Example: 22x^{2} -5 + 6x^{2} + 4

## Difficult Worksheet 2

Simplify for each. Students should have a good handle on the use of exponents for these problems. Example: 12x^{2} - 5 + 4x^{2} + 12.

## Difficult Review Worksheet

Review the steps for simplifying an equation, then complete the practice problems. You will need to take this review. Example: x^{2}+8x^{2}+5x^{2}+6x^{2}

## Combining Like Terms Difficult Quiz

This quiz will help you understand how to simplify expressions. For each problem, simplify. Then check your answers and record your total score below. Example: 15x^{2} - 10 + 3x^{2} + 15

## Difficult Do Now

This worksheet is great to kickoff a class period. Complete the following problems, then put your answer in the "My Answer" box. Example: 8x^{2}+50 - 4x^{2} - 2x = _____

## Combining Like Terms Simple Lesson

These are more simple problems to work with. Follow along and simplify this type of expression: (-7 + 3y) - (2y - 3)

## Simple Worksheet 1

For each, simplify the given equation. Some of these problems with get you going in the right direction. Example: 5n - 2(5-2n) + 2(4n-5) + 10 (4n - 2)

## Simple Worksheet 2

Break these down into digestiable pieces for yourself. Start by putting things to together. Example: 14n - 2(2-3n) + 4(3n-1) + 2(4n-6)

## Simple Combinations Review

Review the steps for simplifying an equation with one variable: (-4 + 2y) - (6y - 4)

## Simple Like Terms Quiz

For each problem, simplify the given equation. Then check your answers and record your total score below. Example:

## Simple Do Now

We label these as "simple", but they include many terms, so they may be a challenge for some students. Example: 7x + (x-5) + 3x - (2x-5) + 6x +2 =

## Solving Equations (combine like terms) - Worksheet 1

Solve for each given equation by putting together all of the coefficients. Example: 10 + 6x + 2x = 18.

## Worksheet 2

Solve for each given equation. There are 10 on this page. Example: 7x + 5 + 3x = 85

## Solving Equations Worksheet 3

These can be done pretty quickly. Example: 6x + 2 + 4x = 122

## Worksheet 4

We are working to get everything to the other side of the equals sign. Example: 92 = 7x + 3x + 2

## Worksheet 5

You wanted more practice and you got it! Example: 6 + 7x + 3x = 46

## Worksheet 6

We made the base numbers very similar, don't get tricked. Example: 28 = 2x + 2x + 4

## Solving Equations (combine like terms-with negatives) - Worksheet 1

Don't get tripped up by the operators here. Example: 3x + 9 - x = 15

## Worksheet 2

This are setup a little more straight forward. Example: 89 = 5x + 5x - 1

## Worksheet 3

You will find a whole bunch of negative values here. Example: - 3x - 1 + 5x = - 9

## (with negatives) - Worksheet 4

The negative values get a little harder to work with here. Example: 3 = -2x + x + 3

## Combining Like Terms Lesson

Follow along with the steps below to solve this equation: (4x+7y) - 2(-3y + 2x). You will need to expand everything to get it going.

## Try the Skill

These can be used with more advanced learners: 3(n+7) + 8(3n+4) + 12(2n-4)

## Practice the Skill

Simplify each equation as we show you in the first example. Example: 3(a+2) + 4(2a+5) + 8(4a-2)

## Negatives Practice Worksheet

Simplify each equation shown. Example: 13m - 11m - 12m + 10m + 16 - 7 + 9m - 5m

## Show the Skill

See if you are ready to be a show off yet. Example: 20m - 12m - 14m + 8m + 11 - 6 + 3m - 2m

## Skill Warm Up

Remember to underline as needed. Example: 17m - 15m - 10m + 9m + 14 - 2 + 8m - 4m

## Meet the Skill 2

Do not let the exponents get in your way. An example problem here: -3x^{2} - 4x + 3 + x^{2} + 8x - 2

## Try the Skill 2

The exponents should not scare you here: -18x + 13 + x^{2} - 9x + 11

## Practice the Skill 2

Simplify each equation shown. Example: 5x^{2}+ 14 - 3x^{2} + 6

## Easy Practice Worksheet

Have another go at this one. Example: -8x + 35 - 9x + 13 + x^{2}

## Show the Skill 2

Simplify each equation that is shown. Example: 7x^{2}+ 13 - 4x^{2} + 8

## Warm Up 2

This one allows you a great deal of room to move around with. Example: -26x + 16 + x^{2} - 14x + 18

## Complete the Equation Basic skills: Independent practice 1

These are perfect to get started with working on multiple terms that need to be packed together. Example: 12x + 5 + 5x + 4

## Independent Practice 2

Solve each equation. You will work with basic terms and constants. Example: 12a + 15 - 9 - 3a

## Intermediate Skills: Independent Practice 1

We introduce how to handle terms that have exponents. Example: 12x^{2} + 5y^{3} + 6x^{2} + 7y^{3}

## Like Terms Lesson

Learn how to group like terms in more complex expressions such as: a + a 3a - a 5a^{4} / a^{2}

## Like Terms - Try the Skill

For each problem simplify by grouping all terms in the given expressions. Example: y x y x y

## Like Terms - Practice the Skill

More practice sheets to move forward with this skill. Example: e + e 3e + 2e e^{2} x e^{2}

## Practice the Skill Twice

We stripped out most of the exponents. Example: y + y 3y + 2y 3y x y

## Show the Skill

We introduce quotients to this for you. Example: 6g ÷ 2 2g x 2g x 2g 8g^{3} ÷ g

## Warm Up

A great way to get students off and running. Example: 4a + 2a 6a^{6} / 3a^{2}2a^{4}

## Same Variable and Power Lesson

We walk you through the process of organizing these guys: a × a, a^{2}, a^{3}

## Worksheet 1

Time to work on this topic at an advanced pace. Example: f × f x f^{2}x f^{3}

## Worksheet 2

You have to group all these terms into five different groups. Example: a × a a^{2} a^{3}

## Review Sheet

You are first reminded about the skill and then asked to work on your own. Then complete the practice problems. b × b x b^{2} x b^{3}

## Like Terms Quiz 2

For each problem, group the like terms, and then check your answers and record your total score below. Example: r × r x r^{2} x r^{3}

## Do Now Basic Skills

Start slowly here, if you get tripped up. Example: g × g x g^{2} x 3g - 2g

## How to Combine Like Terms in Math

Before we get into like and unlike terms in math, it is essential to look at algebraic expressions quickly. An algebraic expression is a mathematical expression that includes constants and variables and operators like addition and subtraction.

A variable is used for a term that’s value is not known, whereas the value of a constant term is definite. A variable usually comes with a numerical number known as a coefficient. Some examples of such algebraic expressions include 2x + 3x – 5, 5x – 10, 5x^{2} - 3xy + 8, etc.

Two like math terms have the same variables. This could be the base number or variable. It could also be a base variable that has the same exponent. As we advance with this skill, we will learn that coefficients can be different in like terms. For example, the value -4yz^{2} and yz^{2}/3 are like terms. In order to solve equations and expression, you will combine like terms often. Often it the first step to solve just about anything in algebra. Be sure that you carry any math operator that is attached to the term. For example: 4y + 7x - 5y + 3x. The 5y carries the negative operator with it. When we combine this, we will end up with -1y + 10x. I like to urge students to underline like terms. If you have two like terms that involve the variable x and y, I would have them underline the x terms once. This would be followed by underlining the y terms twice.

**Like Terms- What are They?**

In an algebraic expression, terms are commonly differentiated by additional or subtraction. For example, there is only one term for a monomial expression. For instance, 5x, 3y, 6x, etc. Similarly, there are two terms in a binomial expression, such as 3y + x, 4x + 5, x + y, etc. There are three terms in a trinomial, while polynomials have several terms if they are of higher degrees.

In algebra, like terms are those that have identical variables and exponents, whatever their coefficients might be. In an algebraic expression, like terms are combined so that it is not difficult to calculate the result of the expression.

For instance, 6xy + 7y + 7xy is an algebraic equation. The terms of this equation are 6xy and 7xy. Hence, if you want to simplify this expression, you can combine the terms 6xy + 7xy + 7y = 13xy + y. it must be kept in mind that when you combine like terms in math, only the coefficients of the terms will be added.

Unlike terms, on the other hand, they do not have identical exponents and variables. For instance, an expression 9x + 4y contains terms because it has different variables that have not been raised to a similar power.

**How to Combine Like Terms in Math**

Now that you understand the theory, let’s learn how to combine like terms in math with some examples:

**Example 1**

Look at this expression: 3x + 4y

Since x and y have different variables, it is impossible to simplify this expression.

**Example 2**

If you want to simplify this expression 3x^{2} + 4x + 8y + 4x + 10x^{2}, here is what you will have to do:

First, sort the terms so that your expression looks like this: 10x^{2} + 3x^{2} + 4x + 4x + 8y.

Then, solve the expression so that it comes to 13 x^{2} + 8x + 8y.

We can solve this expression because the terms have the same variables that have been raised to the same exponent as well.

**Conclusion**

When looking at like terms in math, all you need to keep in mind is that terms that have the same variables, as well as the same exponents are those that can be solved. With like terms, two things can be added or subtracted, depending on the kind of equation you are dealing with.

For example, you know that you can add the terms 3 + 4, and you will be left with a final answer, 7. The reason why you can solve this expression is that both the terms are numerical. Using the same logic, you cannot combine 2x + 3y because these are not like terms, meaning the expression will have to remain unsolved.