A Free Printable Combining Like Terms Worksheet

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Combining Like Terms | 7th Grade | Mathcation

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Key Points

Combining like terms is a fundamental concept in algebra that involves simplifying expressions by adding or subtracting the terms that are alike.
To combine like terms, one must understand what a term is and what like terms are.
Learning how to combine like terms is essential in algebra, as it is used to simplify expressions and solve equations.

Here’s how to Combine Like Terms

Combining Like Terms is a way to simplify algebraic expressions or equations. When Combining Like Terms, what you are trying to do is to combine all of the terms with the same variable together with each other, or any constant term together. In order to do this you are going to either add or subtract the terms with one another. When doing this you will add or subtract the coefficients on the variables with other terms that have the same variable. If the term does not have a variable it is called a constant. All constants are like terms and can be added or subtracted from each other. The last step when Combining Like Terms is to ensure that the expression has been fully simplified.

Combining like terms is a fundamental concept in algebra, which involves simplifying expressions by adding or subtracting the terms that are alike. The process of combining like terms is used to simplify complex expressions and make them easier to solve. It is an essential skill that students must learn to excel in algebra and higher-level math courses.

To combine like terms, one must understand what a term is. A term is a mathematical expression that consists of a constant or a variable or a product of both. Like terms are terms that have the same variables raised to the same power. For example, 2x and 5x are like terms, and 3x^2 and 6x^2 are also like terms. Combining like terms means adding or subtracting the coefficients of the like terms while keeping the variables and exponents the same.

Learning how to combine like terms is essential in algebra, as it is used to simplify expressions and solve equations. This concept is used in various algebraic operations, including the distributive property, factoring, and solving equations. Understanding how to combine like terms is a crucial step towards mastering algebra and other higher-level math courses.

Common Core Standard: 7.NS.1
Related Topics: Distributive Property, Two Step Equations, One Step Inequalities, Two Step Inequalities, Multi Step Inequalities
Return To: Home, 7th Grade

Combining Like Terms Worksheet

How do you Combine Like Terms?

Combining like terms is a fundamental algebraic skill that involves simplifying expressions by adding or subtracting terms that have the same variables and exponents. The process of combining like terms is essential to solving algebraic equations and simplifying complex expressions.

To combine like terms, you need to follow these steps:

Identify the terms that have the same variables and exponents.
Add or subtract the coefficients of the like terms.
Write the simplified expression.

For example, consider the expression 3x + 2x + 5y - 4x - 2y. To combine like terms, you need to group the terms with the same variables together.

3x + 2x - 4x + 5y - 2y

Now you can add or subtract the coefficients of the like terms as follows:

(3 + 2 - 4)x + (5 - 2)y

This simplifies to:

x + 3y

Another example is 4a + 2b - 3a - 5b + 6c.

4a - 3a + 2b - 5b + 6c

Then, add or subtract the coefficients of the like terms:

(4 - 3)a + (2 - 5)b + 6c

This simplifies to:

a - 3b + 6c

It is important to note that only like terms can be combined. Like terms are terms that have the same variables and exponents. For example, 3x and 5x are like terms, but 3x and 5y are not like terms.

In addition, when combining like terms, you need to pay attention to the signs of the coefficients. If the coefficients are positive, you can add them together. If they are negative, you can subtract them.

In summary, combining like terms is a crucial algebraic skill that simplifies expressions by adding or subtracting terms that have the same variables and exponents. By following the steps outlined above, you can simplify complex expressions and solve algebraic equations with ease.

How to Combine Like Terms with Variables

Combining like terms with variables is a fundamental algebraic skill that simplifies expressions and makes them easier to solve. The process involves adding or subtracting terms that have the same variable and exponent. Here are the steps to combine like terms with variables:

Identify like terms: Look for terms that have the same variable and exponent. For example, 3x and 5x are like terms, but 3x and 5x^2 are not.
Add or subtract the coefficients: Once you have identified the like terms, add or subtract their coefficients. For example, if you have 3x + 5x, you can add the coefficients 3 and 5 to get 8 and write the simplified expression as 8x.
Distribute the coefficient: If the expression has parentheses, distribute the coefficient to each term inside the parentheses before combining like terms. For example, if you have 2(3x + 4y), you can distribute the coefficient 2 to get 6x + 8y before combining like terms.
Simplify the expression: After combining like terms, simplify the expression by collecting any remaining terms. For example, if you have 2x + 3y + 5x – 2y, you can combine the like terms 2x and 5x to get 7x and the like terms 3y and -2y to get y. The simplified expression is 7x + y.

It is important to note that when combining like terms, the variable and exponent remain the same. Only the coefficients are added or subtracted. Also, it is essential to pay attention to the signs of the coefficients when adding or subtracting them.

By following these steps, anyone can combine like terms with variables and simplify algebraic expressions. It is a crucial skill that is used in various areas of mathematics, including algebra, calculus, and differential equations.

How to Combine Like Terms with Coefficients

When combining like terms with coefficients, it is important to remember that the coefficients are simply the numerical values in front of the variable. To combine like terms with coefficients, follow these steps:

Identify the like terms: Like terms are terms that have the same variable part. For example, 2x and 3x are like terms, but 2x and 3y are not.
Combine the coefficients: Once you have identified the like terms, add or subtract their coefficients. For example, to combine 2x and 3x, you would add their coefficients to get 5x.
Combine any constants: If there are any constants in the expression, combine them as well. For example, to combine 2x + 3x + 4, you would first combine the like terms to get 5x, and then add the constant 4 to get the final answer of 5x + 4.

It is important to note that when combining like terms with coefficients, you should always keep the variable part of the term the same. For example, if you are combining 2x and 3x, you would combine the coefficients to get 5, and then keep the variable part as x to get the final answer of 5x.

Another thing to keep in mind is that when there is a negative coefficient, it is important to remember to subtract that term instead of adding it. For example, to combine -2x and 3x, you would subtract their coefficients to get 1x or simply x.

In summary, combining like terms with coefficients involves identifying the like terms, combining the coefficients, and combining any constants. Keeping the variable part of the term the same and remembering to subtract negative coefficients, when necessary, is crucial for correctly combining like terms.

Combining Like Terms with Exponents

When combining like terms with exponents, the key is to identify which terms can be combined. Terms are considered “like” if they have the same variable and exponent. For example, 3x^2 and 5x^2 are like terms, while 3x^2 and 5x^3 are not.

To combine like terms with exponents, follow these steps:

Identify the like terms in the expression.
Add or subtract the coefficients of the like terms.
Keep the variable and exponent the same.

For example, consider the expression 4x^2 + 2x^2 – 3x^2. The first two terms, 4x^2 and 2x^2, are like terms because they have the same variable and exponent. To combine them, add their coefficients: 4 + 2 = 6. The resulting expression is 6x^2 – 3x^2, which simplifies to 3x^2.

It’s important to note that when combining like terms with exponents, the variable and exponent should not be changed. For example, 3x^2 and 3x^3 are not like terms, even though they have the same variable. They cannot be combined because they have different exponents.

In some cases, it may be necessary to distribute a coefficient before combining like terms with exponents. For example, consider the expression 2x(3x^2 + 4x^2). To combine the like terms, first distribute the coefficient 2x: 2x(3x^2 + 4x^2) = 6x^3 + 8x^3. The resulting expression is 14x^3, which cannot be simplified further.

Overall, combining like terms with exponents is a fundamental skill in algebra that is used frequently in higher-level math courses. By following the steps outlined above, students can simplify expressions and solve equations more efficiently.

Solve Combining Like Terms Examples in 5 Simple Steps

Determine which terms are Like Terms by looking at the variables of the terms.
If the terms have the same variable, then they are Like Terms.
If the term does not have a variable it is called a constant and is a Like Term with other constants.
Simplify the expression by adding or subtracting all Like Terms.
Finally, ensure the expression is fully simplified.

Combining like terms is an essential skill in algebra that simplifies expressions by adding or subtracting terms with similar variables. This section provides some examples of combining like terms to help students grasp the concept.

Example 1:

Simplify the expression: 3x + 4y – x – 2y

To combine like terms, add or subtract the coefficients of the terms with the same variable. In this case, we can combine 3x and -x to get 2x, and 4y and -2y to get 2y. Therefore, the simplified expression is:

2x + 2y

Example 2:

Simplify the expression: 5x^2 + 3x – 2x^2 – 4x

To combine like terms with exponents, first identify the terms with the same variable and exponent. In this case, we have 5x^2 and -2x^2, which can be combined to get 3x^2. Next, we have 3x and -4x, which can be combined to get -x. Therefore, the simplified expression is:

3x^2 – x

Example 3:

Simplify the expression: 2x^2y + 3xy^2 – 4x^2y + xy^2

To combine like terms with multiple variables, identify the terms with the same variables and exponents. In this case, we have 2x^2y and -4x^2y, which can be combined to get -2x^2y. Next, we have 3xy^2 and xy^2, which can be combined to get 4xy^2. Therefore, the simplified expression is:

-2x^2y + 4xy^2

These examples illustrate how to combine like terms by adding or subtracting the coefficients of terms with similar variables. It is important to note that only terms with the same variable and exponent can be combined.

5 Quick Combining Like Terms Practice Problems

Combining Like Terms Definition

Combining like terms is a fundamental concept in algebra that involves simplifying an expression by adding or subtracting terms that have the same variables and exponents. In simple terms, it involves grouping together terms that have the same variables and adding or subtracting their coefficients to form a single term.

In mathematical terms, two or more terms are considered like terms if they have the same variables and exponents. For example, 3x and 5x are like terms because they have the same variable (x) and exponent (1). Similarly, 2x^2 and 6x^2 are like terms because they have the same variable (x) and exponent (2).

On the other hand, terms that have different variables or exponents are not like terms. For example, 3x and 4y are not like terms because they have different variables (x and y), while 2x^2 and 3x^3 are not like terms because they have different exponents (2 and 3).

Combining like terms is an essential skill in algebra, as it simplifies expressions and makes them easier to work with. It is often used in solving equations and simplifying complex expressions.

It is important to note that combining like terms is not the same as simplifying an expression. Simplifying an expression involves performing a series of operations to reduce it to its simplest form, while combining like terms is just one step in the simplification process.

In summary, combining like terms is a process of simplifying algebraic expressions by grouping together terms that have the same variables and adding or subtracting their coefficients to form a single term. It is an essential skill in algebra and is used extensively in solving equations and simplifying expressions.

Distributive Property and Combining Like Terms

The distributive property is a fundamental concept in algebra that is used to simplify expressions. It states that when a term outside of a set of parentheses is multiplied by each term inside the parentheses, the result is the same as if each term inside the parentheses was multiplied by the term outside of the parentheses and then added together.

For example, if you have the expression 3(x + 4), you can use the distributive property to simplify it to 3x + 12. This is because 3 multiplied by x is 3x, and 3 multiplied by 4 is 12.

Combining like terms involves adding or subtracting terms that have the same variables raised to the same power. For example, 3x + 2x can be simplified to 5x. The distributive property can be used in conjunction with combining like terms to simplify more complex expressions.

For instance, consider the expression 4(2x + 3y) - 2(x - y). To simplify this expression, you would first use the distributive property to multiply 4 by each term inside the first set of parentheses:

4(2x + 3y) = 8x + 12y

Next, you would use the distributive property to multiply -2 by each term inside the second set of parentheses, remembering to distribute the negative sign:

-2(x - y) = -2x + 2y

Finally, you would combine like terms by adding the terms with the same variables raised to the same power:

8x + 12y - 2x + 2y = 6x + 14y

As you can see, the distributive property and combining like terms are powerful tools that can be used to simplify even complex algebraic expressions. By mastering these concepts, students can make significant progress in their algebra studies and gain a deeper understanding of the subject matter.

FAQ about Combining Like Terms

How do you combine like terms and simplify?

To combine like terms, you add or subtract the coefficients of the terms that have the same variables. For example, if you have the expression 3x + 5x, you can combine the like terms by adding the coefficients of x. So, 3x + 5x = 8x. To simplify an expression, you combine the like terms and perform any necessary operations.

What is an example of combining like terms?

An example of combining like terms is 2x + 3x + 5x. To combine the like terms, you add the coefficients of x, which are 2, 3, and 5. So, 2x + 3x + 5x = 10x.

How do you identify like terms?

Like terms have the same variables with the same exponents. For example, 3x and 5x are like terms because they have the same variable x. However, 3x and 5y are not like terms because they have different variables.

Does combining like terms come first?

Combining like terms is one of the first steps in simplifying an expression. However, it depends on the specific problem and the order of operations. In some cases, you may need to perform other operations before combining like terms.

What is an example of a like term?

An example of a like term is 4x and 5x. Both terms have the same variable x with the same exponent of 1.

How can you use the distributive property to combine like terms?

The distributive property allows you to simplify expressions by multiplying a factor to each term in parentheses. For example, if you have the expression 3(x + 2y), you can use the distributive property to simplify it to 3x + 6y. Once the expression is in this form, you can combine like terms.

How do you combine like terms in 6th grade?

In 6th grade, students learn to identify like terms and combine them by adding or subtracting their coefficients. They also learn to simplify expressions by performing any necessary operations.

How do you combine like terms in 7th grade?

In 7th grade, students continue to practice combining like terms and simplifying expressions. They may also learn to use the distributive property to simplify expressions.

How do you combine like terms in 8th grade?

In 8th grade, students further develop their skills in combining like terms and simplifying expressions. They may also learn to solve equations involving like terms and to use variables to represent unknown quantities in real-world problems.

Combining Like Terms Worksheet Video Explanation

Watch our free video on Combining Like Terms. This video shows how to solve problems that are on our free Combining Like Terms worksheets that you can get by submitting your email above.

Watch the free Combining Like Terms video on YouTube here: Combining Like Terms Video

Video Transcript:

This video is about how to combine like terms. You can get the combine like terms worksheet used in this video for free by clicking on the link in the description below.

Before we do any practice problems from our combining like terms worksheet, I wanted to briefly go over what a like term actually is. Now there are a couple ways to identify like terms and I’m going to go over the most common. Any term that has the same variable combination is a like term. First of all, a variable is any letter that’s used to represent a number. Typically this would be like X or Y.

You will usually see in math class but it could also be a combination of variables. It could be like x and y put together, sometimes you’ll see a B as a combination or M n. Sny term that would have some type of variable or variable combination would be a like term with any other term that had the same variable or the same variable combination.

The other type of like terms is what are called constants. Now a constant is just a fancy math way of saying any plain old regular number. This would be anything that’s a number. It could be like 3 and 5 and 11. Those are all going to be like terms and anytime you have numbers in your problem or in your expression, they are automatically like terms, and you can combine them.

Let’s jump to the first problem on our combining like terms worksheet. Number 1 gives us 1 plus 4 X plus 3. Remember a like term or any terms that have the same variable combination or if they are constants or numbers. In this case we have a 1 and we have a 3 in our expression and because they are constants they can be combined together. And the second type of term we have is this for X and this for X has no other term with X’s.

It doesn’t get added to the constants because this has a X this is its own like term and these do not have X’s. You cannot combine the 4x with the 3 or the 1 because they also do not have X’s. All you’re actually going to combine is the 1 and the 3 so this 4x comes down. We have 4x here and then we have to combine 1 + 3 + 1 + 3 is 4. Our solution is 4 X + 4.

Jumping down to number 3. We have negative 3x minus 5 plus 6. In this case we have like terms but they are the terms that have the x’s. This negative 3x and this 6x are like terms because they both have the variable combination of the X. Now this minus 5 in this case is not a like term with anything else because there is no other constant in this expression to combine it with. What we’re going to do is we’re going to combine negative 3x + 6 X, and negative 3x + 6 X is positive 3x and then this minus 5 or this negative 5 comes straight down. Our solution is 3x minus 5.

The next problem to show you how to do combining like terms is number 5. This problem gives us 25 plus 11x minus 10 minus 5x. The first thing we have to do is we have to identify which terms are like terms. The way we do that is we look at the problem and we look for terms that have the same variable combination or our constants. In this case, we have 11 X + 5 X and I know that they are like terms because they both have an X and because they both have X’s that means that they’re like terms. You can combine those two together.

The second thing I noticed is that we have constants in this case. We have 25 and we have negative 10. They are both numbers which means that they are automatically like terms. Now we’re going to combine them. I know that 11x minus 5x get combined, 11x minus 5x will give us 6x and then we combine 25 and negative 10 and then we do 25 minus 10 and 25 minus 10 is 15. Our answer is 6x plus 15.

The final problem we’re going to go over for showing you how to combine like terms is going to be number 6. This problem gives us 10 X plus 3 X plus 4 X minus 10. Remember the first thing we have to do is we have to determine which terms are like terms. In this case 10x and 4x are like terms because they both have the same variable which is X and 3, which is a constant or number can be combined with negative 10 because it is also constant and a number.

When we combine these the first thing, we’re going to combine is 10x plus 4x, which is 14x and then positive 3 minus 10 that gives us negative 7. Our final answer for this one is 14x minus 7. Practice these problems by downloading the combining like terms worksheet with answers above.