4.8 Identifying Like Terms

Introduction

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Unit 4

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Unit 6

Math Basics  >  Unit 4 Expressions  >  Lesson 4.8 Identifying Like Terms

Video Lesson

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Practice Activity

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+ Video Transcript

In our last lesson, we learned that terms are parts of expressions that are separated by plus or minus signs. And as we get into our future lessons, we're going to learn different things that we can do with those terms when we come across different types of algebra problems. But before we do that, it's important for us to be able to identify like terms. So what are like terms? They're terms that have the same variable and the same exponent with that variable, if there is an exponent at all. All constants are considered like terms because they are made of only numbers. So whenever you see two terms that are just numbers, and remember if it's just a number we call them constants, then they are considered to be like because they are made of just numbers, no variables. Now let's look at sets of examples to be able to figure out whether two terms are like or if they are not like. Okay, here's our first example. Are these like terms? We have 21 and 6.5. They're both just numbers. They're constants. So in this case, yes, they are like terms because they are both constant terms. Now we see some variables. Here we have a five x and an eight Y. Are they like terms? Well, we said that like terms have to have the same variable and these don't. We have five x and 8y.  X and Y are two different variables. So no, these are not like terms because they have different variables. Now we have ten x and ten. So like terms have to have the same variable, we said earlier. Now both of these have the same number in there, but they're not the same type of term. The ten x has the variable x with it and on the right we have just the number ten, which is a constant. So no, these are not like terms because the first one has a variable and the second does not. Now we have two x and eight x squared. Are they like terms? Well, they both do have x. They have the same variable. But if you remember what we said earlier, they have to have the same variable with the same exponent. So if there's exponents with that variable, they have to have the same exponent for them to be considered like terms. Otherwise they are not like. They are different kinds of terms. So no, these are not like terms. Now we have seven x and three x. They both have the same variable x. They have different numbers, different coefficients. But that's okay. They can have different coefficients. When we're trying to figure out if terms are like or not, we're really just paying attention to the variable part. If there's a variable there, they have to have the same thing going on with their variable in order for them to be like terms. So yes, these are considered to be like terms because they do have the same variable. It's okay that they have different coefficients.

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