In our last lesson, we learned what it means for terms to be like. We learned how to identify like terms. In this  lesson, we're going to learn how to combine like terms. Now, combining like terms is used to simplify expressions, which really just means we're going to write the expression over, but just in a shorter, more efficient way. And that really means that we're just going to add the like terms together. Now remember, like terms are terms that have the same variable and the same exponent with that variable. And all constant terms, which are the terms that are just numbers, are considered like terms. In our first example, we have two x plus three x plus four Y, and we can see that we have three separate terms in this expression. Now, before we combine our like terms, let's pretend that instead of variables x and Y, we have apples and bananas. We have two apples and three apples and four bananas. Wouldn't it make a little more sense or be more efficient to just combine the apples together and say, hey, I have five apples and four bananas? We're representing the same amount of apples and bananas, just representing it in a more efficient or simplified way. And that's really all we're doing when we're combining like terms. But of course, our original problem didn't have apples and bananas, we had x and y. So we would really write this as five x plus four y. Now we'll go over a couple more examples, but we won't use apples and bananas this time. We'll use another little trick that will help us be able to combine like terms easily. So let's see what we have here. We have eight x plus six plus two x minus one. So we want to see what kind of terms we have here and see if we can find any that are like terms. Remember, terms are all separated by a plus or minus sign. So we have four separate terms here. Do we have any like terms? I think we do. We have an eight x and a two x. They're like terms because they both have the same variable, x. It's okay that their number coefficient is different. They're like terms as long as they have the same variable. Now notice that I included the plus sign with the two x when I put my box around them. So that's one tip that I want you to remember. Include the symbol to the left of the term. And I like to use these boxes to help me be able to visually see which terms go together. So in this presentation, I'll use boxes that are different colors. So if you have different colored pencils or markers, you can use that. Or you can even draw different shapes around the like terms like boxes or circles, just some type of visual way for you to see which ones go together. So I have eight x, and since I included the plus sign that's to the left of the two x, I can see I have a positive two X there. When I add those together, I get ten x. So we've combined like terms. Not too bad, right? Let's see what other like terms we can combine. I have a positive six and a negative one. I'm going to treat that subtraction sign as a negative one. Now, when I add those two terms together, positive six and a negative one, that gives me positive five. And all I have to do is write it down right next to the ten X. I have ten X and positive five, which, of course, we would just read as ten X plus five. And we just simplified this expression by combining like terms. We found a way to write it in a simpler, more efficient way. Let's look at one more example. Twelve M squared minus three M plus four M squared. Now, this time we have three terms. Let's see if there are any like terms. Now, they all have the same variable. They all have the variable M. But the first and last term have the exponent of two with the M, and the term in the middle does not. So that means that the first and last terms are like terms. They both have the same variable with the same exponent. They both have an M squared. So that makes them like terms. So we can add those terms together, which means I'm just adding the coefficient parts together. So twelve squared plus four M squared will give me 16 M squared. And then that minus three M in the middle. There's nothing else to combine it with, so I just keep it as it is. And my final simplified expression is 16 M squared minus three.