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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After watching this video lesson, you will be able to simplify any subtraction expression by combining like terms. Learn what to look for and how easy this is to do.

In this video lesson, we look at **subtraction expressions**. These are the mathematical expressions with subtraction in them. Specifically, we will look at the subtraction expressions that have terms made up of the product of a number and a letter or variable. This means that we will look at expressions such as 5*x* - 3*x*. It might help you to visualize this problem by looking at the variable as a thing instead of a letter. For example, the *x* could stand for a basketball. If this is the case, then 5*x* means you have five basketballs and 3*x* means you have three basketballs. You see the subtraction sign telling you to take away three basketballs from the group of five. How many basketballs are left? Two basketballs; using the *x* again, we have 2*x*.

A subtraction expression can have more than one variable in it. For example, we could have an expression such as 5*x* - 3*x* - 8*y*. In this case, we simply combine the terms that have the same variable. So, we combine the 5*x* and the 3*x*. Since there is only one term with the *y*, we keep it as is. In math, we call this process **simplifying**. We get 2*x* - 8*y*. We can also visualize problems such as these by picturing different things for different letters. For example, in our problem 5*x* - 3*x* - 8*y*, we can picture motorcycles for the *x* and cars for *y*. Because motorcycles and cars are different, we can't combine them into one big group of like items. Motorcycles and cars are not alike. We can combine the two groups of motorcycles that we have, the 5*x* and the 3*x*. We see subtraction going on, so when we combine these two groups, we are actually subtracting the 3*x* from the 5*x*. We get 2*x* - 8*y* as our simplified expression.

Let's look at a couple of examples to help us understand this process even more.

Simplify: 7*x* - 4*x* - 9.

In this expression, we see two like terms, the 7*x* and the 4*x*. We can go ahead and perform the subtraction here. We get 3*x*. We still have a minus 9, but this -9 doesn't have any other like terms, so we leave it as it is. Our simplified expression then becomes 3*x* - 9.

Simplify: 20*x* - 10*x* - 4*y* - 7*y*.

In this subtraction expression, we have two different letters or variables. How many like terms do we have for each variable? We have two for each. For the *x*, we have 20*x* and 10*x*. We can combine these. For the *y*, we have the 4*y* and the 7*y*. We can combine these as well. We are dealing with subtraction here, so we have to make sure our signs are correct.

- 20
*x*- 10*x*= 10*x* - -4
*y*- 7*y*= -11*y*.

Putting this together gives us a simplified expression of 10*x* - 11*y*. And we are done!

What have we learned? We learned that a **subtraction expression** is a mathematical expression with subtraction in it. To simplify such an expression, we combine like terms. Like terms have the same variable, or letter, with the same exponent. So, 4*x* and 8*x* are like terms because they both have the same letter.

After you have finished reviewing this lesson, you should be able to simplify a subtraction expression by combining like terms.

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6th-8th Grade Math: Practice & Review55 chapters | 469 lessons

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