 This first example, I have 20y plus y. The variable is y. They're both just plain y, so I can combine them and say that I have 21y. I have 20 plus one more y. And this next example, I have negative 12a minus 3, which is not the same, and then a 5a. So these two terms right here are like terms. So I could rewrite this as negative 12a plus 5a minus the 3. Remember, our properties say that we can add any order, so let's add to make it convenient. Now I can combine my like terms. Negative 12a plus 5a is going to be negative 7a, and then my negative 3 is the only constant I have, so I just have minus 3. In this example, I have 2ab plus 7a, and this is simplified. It's simplified because they both have an a in it, but the 7 does not have the b as well, and so they are not like terms. Finally, this last one is a little tricky, but 6y over 5 plus 3y. This is really 3y over 1, so we can see that these are like terms. We can combine those. Now if we're going to combine them, remember it's adding, so we have to get the same denominator. So this common denominator between 5 and 1 is going to be 5. So my first fraction gets to stay. It's 6y over 5. But now I have to multiply the 3y over 1 times 5 over 5. Remember, multiply by a factor of 1, that when you multiply the bottom, it gets you to the least common denominator. But if you do it to the bottom, you have to do it to the top, so 3y times 5 would be 15y over 5. Now I have both denominators the same, and I can add the numerators. So 6y plus 15y all over 5, or 21y over 5. Let's do some more simplifying expressions then. We may have to use the distributed property that we've learned recently. We may have to combine like terms. Use all the things that we know so far to get these expressions simplified. So here's my like terms, they're both x terms. So I'm going to rewrite it. 12x and then take the sign with it. You've got to take that sign with it, so minus x and then minus the 3. To 12x minus 1x, I have 12. You can't think about it as 12 minus 1x minus 3. 12 minus 1 would be 11 times x minus 3. Maybe that's helpful for some of you. In this case, you have to distribute first. So 6 times 5x would be 30x, 6 times negative 10 would be minus 60, and then bring down your minus 10. So our like terms are actually these two constants right here, and they're already lined up together. When you want to write this, I would just come in here and add the opposites. Since it's a bunch of subtraction, it might be easier to say this is plus a negative 60 and plus a negative 10. So we have 30x and then negative 60 plus another negative 10 gives me a total of, you could think of it as plus a negative 70, or you could write 30x minus 70. I take either one. These are the same. Do more problems. Still simplifying. We've got to distribute here, but remember when you distribute, when you have expressions like this, you have to take the sign with it, carry the sign, and distribute to everything inside. So I have the 7. Now it's going to be negative 2 times 3x. So I have negative 6x. And negative 2 times positive 6 would be a negative 12. And then I have like terms again, which are constants, but they're not next to each other. So if it helps us, we're going to write 7 and then take the sign minus 12 and then minus 6x. There's my like terms. 7 minus 12 is a, remember you can subtract. The difference between 12 and 7 is 5, but 12 is larger, so it's negative 5 minus 6x. And that would be a final answer. So here we have 10 times 1 half x, got to distribute first. Remember to always distribute first. So 10 times 1 half x is really 10 times 1 half times x. So that would be 5x. And then 10 times a negative 2 is going to be minus 20. And then plus, but you got to multiply here. Order of operations says multiply before you add and subtract. So 1 half times 10 going to be 5. Here's my like terms. So I have 5x and negative 20 plus a positive 5. The difference is 15 and 20 is larger and it's negative. So 5x minus 15.