 In this video, I'm going to be talking about combining like terms. Your algebra book is going to call this something a little bit different. They might call it simplifying algebraic expressions. I like to call it combining like terms. It's basically the same thing. Now your book calls this an algebraic expression. What is that? Well, an expression is just a math sentence. It's when you take a bunch of numbers and letters and add or subtract or multiply them. That's an expression. Algebraic means you have variables in here. So algebraic expression, I like to call this combining like terms. So this is how I combine like terms. The first thing you got to do is you got to identify what is a like term. Now my definition of what a like term is, is that a like term has the same variable to the same power. Same variable to the same power. Now in this case for this example, I don't have to worry about powers. I don't see any powers. I don't see any exponents up there. So in this case, I'm only looking for the same variables. So as I look through this, I'm going to identify which ones are the same variables. So I'm just going to start at the very beginning. I have a 3x here. And as I look, I'm looking for more x's. So as I look down, I see that there's also a plus 2x, a positive 2x there. Notice I underlined them. When I combine my like terms, I like to identify them. I like to use, I like to underline to make sure that they're the same. I'll simulate with this next one. So going on to identify my next ones, I have a negative 2y here. Negative 2y, that means this one is a y term. So I'm going to put two lines underneath it. And I'm going to look for other y terms. And as I look over here, I see a plus y. Plus y or plus 1y, whatever you'd like to think of it as. So I put two lines underneath that. Now I'm going to continue on to identify any other like terms. Now look here, I see a z. But as I glance to my other terms, I don't have any other z. So I'm not going to label that one at all. I'm just going to go on to my numbers. These are called numbers or constant terms. The reason they're called constants is because these are constantly the same number. 1 is always going to be 1. Negative 4 is always going to be negative 4. It's constant. So instead of just calling them numbers, we'd like to call them constants. Anyway, 1, I'm going to put three lines underneath it. And negative 4, I'm going to put three lines underneath it. This just helps me to identify which terms are alike. So now I'm going to go through, and I'm going to add or subtract, depending on what the signs are. I'm going to add or subtract all my terms. So 3x plus 2x. 3 plus 2 is 5. So I have a ton of little 5x's. Now I'm going to go to my y's. Negative 2y and plus 1y. Negative 2 plus 1 is going to be a negative 1y. Now you might put negative 1 there. I just put y. Negative y, negative 1y, it's the same thing. I just don't put the 1 there. Most of your textbooks, most mathematicians, most anybody is not going to put a 1 there. So that's what I'm going to simulate this as. OK, moving on. The 4z, there's no other z, so I'm just going to simply rewrite this. It's plus 4z. And then now, last but not least, I have 1 minus 4, positive 1 minus 4, which ends up being negative 3. So that is a short version of combining like terms. And again, you have to have the same variables to the same power. In this case, I didn't have to worry about powers, but that's combining like terms. No other terms here are like that, my x's, my y's, my z's, and my constants. So that is my simplified expression, my simplified algebraic expression. So let's do another example, something a little bit more difficult, something a little bit more difficult. Let's try negative 3, and then in parentheses, 2x minus xy plus 3y, I have to forgive me by looking through a book here, minus 11xy. There we go. This one's a little bit more confusing, but this is going to help me to reiterate my point that when I combine like terms, like terms have to have the same variables and the same powers. OK, so on this example, now this example is a little bit different because I have the parentheses there, so I have to evaluate that first. I have to take that negative 3 that is out front, and I have to multiply it all the way through. So I'm going to use another color. Take negative 3 times the first, the second, and the third terms. This is what we call distributive property. This is what we call an application of the distributive property. So I'm going to multiply this. OK, so negative 3 times 2x is negative 6x. Negative 3 times negative xy is going to be a positive 3xy. And negative 3 times 3y is going to be a negative 9y. And then this guy on the end, we just bring him down, negative 11xy. So notice with this distributive property, I'm just multiplying by negative 3. So all it really affects is the signs and the numbers. It doesn't affect the variables. Notice x here, xy, and y, that really didn't change, but it's the numbers that changed, the numbers that changed. All right, so now after I've done the distributive property, I have to identify which terms are alike. This is an x term. It just has an x variable. As I look, I see other x's, but it's not alike. Remember, I have to have the same variables and the same powers. I don't have the same variables. I don't see any other x terms. So moving on, 3xy, if I look here, I have a positive 3xy and a negative 11xy. Those ones are like terms because they have an x and a y. So I can actually combine those. And to continue on, this is a y term. I don't have any other y terms. So that one's just going to stay as it is. Now to rewrite this, negative 6x. The x's stay the same. xy's 3 minus 11 is negative 8xy. And then I have my y's and x's, which is negative 9y. Now when you rewrite this, usually you want to put these in alphabetical order. So notice here that I have my x's first, then my xy's, then my y's. So notice that with two variables, I have my x's to the left, and then my y's to the right, and any combinations are going to be in the middle. That's how you normally would write this. It doesn't really matter, actually, which order you write this in. But that's normally how everybody writes it. Those are two examples of combining like terms. The one thing to remember is when you combine like terms, you have to have the same variable and the same power in your terms. And then you simply just need to add or subtract the coefficients, which are the numbers out front.