A Free Printable Combining Like Terms Worksheet

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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.

Common Core Standard: 7.NS.1

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Breaking Down the Combining Like Terms Definition

Combining Like Terms is an approach to solve mathematical expressions or equations. When Combining Like Terms, what you are attempting to do is to consolidate the majority of the terms with other similar terms together with one another, or any numbers together. You are going to either add or subtract the terms with each other. While doing this you will include or subtract the coefficients with different terms that have a similar variable. When the term does not have a variable it is known as a constant. All constants resemble terms and can be included or subtracted from one another. The last advance when Combining Like Terms is to guarantee that the expression has been completely solved.

5 Quick Steps to answer any Combining Like Terms Examples

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 Practice Problems

Watch the video explanation of our Combining Like Terms Worksheet

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. Temember 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.