Simplifying Expressions with Like Terms

[The video starts with the title of the video in a yellow box. The title is “Simplifying Expressions with Like Terms”] 

Narrator: Welcome to the video on simplifying expressions with like terms.

[Another yellow box appears. Inside says “What are terms?”] 

Narrator: So what do we mean by like terms? Here we see an expression [refers to the equation narrator is about to mention], three W plus four W. Each of these is a term. The three W is a term, and four W is another term.

[Another yellow box appears. Inside says “like terms are equal to terms whose variables are the same”] 

Narrator: What we mean by like terms are terms whose variables are the same. So, for example, three W and four W are like terms because they both have the same variable and this variable is to the same power. It’s just a W, not W squared, it’s not W cubed, it’s just W. Here’s another example of like terms, two Y cubed and just Y cubed. Y cubed is the same as, actually, one Y cubed. So this is two Y cubed and one Y cubed. Because they both have the same variable to the same power of three, they are like terms, and the thing with like terms is that we can combine them. So we can add together their coefficients, or this number in front of them.

 [another yellow box appears. Inside the box says “coefficient is equal to number in front of variable. It is multiplied to the variable.”]

Narrator: So, three W plus four W equals seven W. Let’s just quickly look at why that works.Well, three W is the same as W plus W plus W, and four W is the same as W plus W plus W plus W. And then, if we’re adding those together, we are adding all of these W’s together, which is seven W’s, so that’s the same as seven times W.

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Narrator: Now, remember what I was saying about variables with the same power. Two Y cubed plus Y cubed is the same as Y cubed plus Y cubed, and one Y cubed, here because if we don’t have a coefficient, a coefficient is the number in front of a variable, if we don’t have a coefficient in front of a variable, we just know that it means one. So this is the same as Y cubed, and we’re adding them all together, so that equals three Y cubed. So two Y cubed plus Y cubed equals three Y cubed. So here’s another expression, and in this expression we have terms with the variable W and we also have terms with the variable Y cubed. We know that W’s and Y cubes can’t go together. They’re just different, but the three W and the negative W can go together, so this is the same as three W minus W, and this is the same as four Y cubed minus Y cubed, so plus four Y cubed minus Y cubed. So three W minus W is the same as two W because three minus one is two, and then they’re both W’s, and four Y cubed minus one Y cubed is the same as a positive three Y cubed. And that is as far as we can simplify this. We can’t combine these terms, because they have different variables in them.

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Narrator: So what about an instance where we have W and W squared? For example, three W plus two W squared. Again, we cannot actually add these terms together because W squared is different than W. Now, here’s another example. In this example, we have a lot of different steps that we’re going to have to take before we can start combining like terms. First of all, we see that there are several terms, but they’re encased in parentheses. Because they’re in the parentheses, for example, we can’t add the two and the negative one because they’re both in parentheses, and according to the order of operations, we have to do everything in parentheses first. So when you come across a problem like this, just start doing it step-by-step using the order of operations. So the order of operations says that we do everything in parentheses first. Well, two minus three B. Two is one term and negative three B is another term, but we can’t combine them because of this B. This B is in this term, but it’s not in the term with two, so we can’t combine them. So this set of parentheses is as reduced as it can be. The same is true over here. B minus one can’t be reduced anymore, it can’t be combined, because one does not have a B while the term B does, they cannot be combined either. So the next thing we can do, though, is do exponents. There aren’t any exponents, so then we go onto multiplication. Now we have multiplication out here in front of each set of parentheses. The four is being multiplied to everything within the parentheses, and this is where we use our distributive property of multiplication. So the four gets multiplied to the two and to the negative three B. So let’s do that first. So four times two, and then we have four times a negative three B. Well, four times negative three times B. These are our terms, and the sign is going to be indicated by the sign of this term. So four times negative three is negative twelve B, and four times two is eight. So we have eight minus twelve B, now let’s go over to this side. This is two times B and two times a negative one, so we have two times B and two times a negative one. So two times B is two B, and two times negative one is negative two. So now we can combine like terms. Well, we have a negative twelve B and a two B right here, so negative twelve B plus two B is going to give us a negative ten B and eight minus two, or eight plus a negative two, is six, so plus six, and that would be our answer. That’s as far as we can simplify this because we cannot put these terms together because the six doesn’t have a variable B in it.

[end of video]