 This is a video of more examples of combining like terms sometimes combining like terms can be a little bit tricky So I'm just going to do a few more examples in this case this Algebraic expression that I have 4x squared y to the third minus 3y squared plus 4x squared minus 2x squared y cubed You'd also say cubed instead of to the third like I said earlier Okay, in this case. I want to identify those terms that have the same variables to the same power That's that's how I that's how I explain how to combine like terms if they have the same variable and the same power Then you need to add together the coefficients. So let's go through this Okay, so I have this term is an x squared y to the third notice. I'm not even looking at the four I'm just looking at the variables x squared y to the third x squared y cubed you could also say So I want to see if there are any other terms that have just those variables With just those powers. So as I look my next one y squared doesn't even come close Okay, I need x's and y's. So if I look to the next one x squared No, I need x's and y's. I look to the fourth one here x squared y cubed x squared y cubed Is the exact same so these two are like terms those two are like terms They have the same variables to the same powers now. I need to add or subtract the coefficients four minus two is two Notice that the coefficient changes But the exponents and the variables they do not change x squared y to the third x squared y to the third x squared y to the third the Variables and the exponents did not change. It was only the coefficients Alright, and then looking at these ones again. Don't be confused if these have yes These have the same exponent, but the variables are different. So these two terms here in the middle are not alike They're not the same. I cannot combine those so what I'm going to do is I'm going to just leave this as negative three Y squared plus four x squared Okay, so that is my simplified answer. That's right there as good as it gets Now I mentioned something in a different video about putting these in order You don't have to put them in order. You can put them in order Alphabetical order from left to right so x should probably go first and then the y's after that But honestly, it doesn't matter what order you put them in for now I'm going to say that this is this is okay. This is good The main concept that we want to get here is identifying like terms your two like terms They have the same exponent excuse me same variables To the same powers same variable same power. We want to add or subtract the coefficients Okay, so that's one example of combining like terms Something else another example of combining like terms This one I'm going to write down actually is a distributive property example Which has a variable in it and I'm using different variables here instead of those x's and y's that we commonly refer to J times the quantity 6k squared plus 7k plus 9 jk squared minus 7 jk All right, so this one again a little bit different example a little bit more difficult what we have to do first is we have to Distribute the j first so I have to take this j here and Multiply at times the two terms inside the quantity inside the parentheses sometimes parentheses are called quantities So you'll hear me say that a few times. All right, so now when I multiply time with a variable A couple of things will change not much though. So in this example j This is I'm only multiplying with j only the variables are going to change So the numbers gonna stay six and then when we write these j's and k's together We always try to write them alphabetical order j comes before case. This is gonna be six jk squared That's the first district distribution the second just distribution. It's gonna be seven Jk So again the numbers don't change. It's just the variable parts of them change. Alright, so now I'm gonna write the rest plus nine Jk squared minus seven Jk so now I want to identify anything that is a like so notice here that I have it. Here's a jk squared There is also a jk squared and then I also have jk term and Then over here. I have another jk term So now I've identified those terms that are alike. So now I need to add or subtract the coefficients So let's start with the jk squared six plus nine is 15 jk squared only the coefficients change not the variables or the exponents All right, so that's the first one the second one here seven minus seven is zero jk Okay, now if you get a zero jk that actually just goes away So my final answer is going to be 15 Jk squared that is my final answer Yeah, now a lot of times students you'll recognize students will recognize that the seven Minus seven is zero and so that term is just going to go away Jk it doesn't matter what those numbers are if they multiply times zero you're going to get zero So you're basically adding nothing. All right, so sometimes a lot of our students won't show this step, but that's okay So my final answer there is 15 jk squared again We want to remember when you add like terms you have to have the same variables To the same power if you can identify that then you just simply need to add or subtract the coefficients