If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Intro to combining like terms

In simple addition we learned to add all the numbers together to get a sum. In algebra, numbers are sometimes attached to variables and we need to make sure that the variables are alike before we add the numbers. Created by Sal Khan.

Want to join the conversation?

  • starky ultimate style avatar for user Finn
    Is zero prime, composite or neither?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • mr pants teal style avatar for user SiennaPitbull
    so am i adding the X's for my answer?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user David Yuan
    You had to pick Chuck Norris
    hahahahahahahahahahahahahahahahahaha
    its beautiful!
    but still
    heres my question,
    Could you take the exponents and divide them by itself if one of them is x^2 and it ends up as x=?
    (20 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user Geo.
    Is there a way to understand math better?
    (7 votes)
    Default Khan Academy avatar avatar for user
  • marcimus purple style avatar for user Haughtdogwrelish
    I simply cannot figure out how to do this. I've watched the videos over and over and for some reason, it doesn't translate to the practice questions. I had the same problem in school. This has me doubting everything. Was enrolling in college a mistake? Why have I made near perfect grades in everything else, but this is like some other language?
    (10 votes)
    Default Khan Academy avatar avatar for user
    • blobby green style avatar for user TheNinja
      Yes, it is a very different language. But, to help me, I think of it as two different groups.
      For example; 2x + 3x -7y = ?
      In order for me to understand it, I group them into two different groups; the x's in one group and the y's in the other. I make as many groups as necessary. So, to solve the problem, 2x + 3x are one group, and -7y is another group. Then, I solve each group individually. 2x + 3x = 5x (Don't forget your variable!). -7y has nothing else to work. So, the answer becomes; 5x - 7y.
      Hope that helped!
      (2 votes)
  • leafers seedling style avatar for user Alexander J  Alonso
    How to solve this question 3x + 4 - 7x -6?
    (5 votes)
    Default Khan Academy avatar avatar for user
  • piceratops tree style avatar for user Margie Fischer
    If my question is 20c+10b+25+5+30c, I know that I can add the 20c with the 30c bc the variables are the same, but I dont know what to do with the 10b. Someone please help me-
    (7 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user ramiyah1127
    I've had to go back on this video over and over, I still don't understand. It may be the fact that I'm just stupid and too slow to catch up with everyone else.
    But seriously, here's what I have to say; When you have a simple question, such as this: -n + (-3) + 3n + 5
    How do you solve it? Actually, how do you solve most equations? If anyone has an answer, please help!
    (7 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user V1rtua1F0X
      First, hello Ramiyah! In this video, what Sal is doing is just simplifying things up for the listeners. As you know, 2+3= 5, so 2x + 3x = 5x. A trick to solve this is to move all numbers with same variables to one side and set the other numbers with or without different variables to another. As an example, 3x + 7x +3 -6 + 8x. To solve, first move all numbers with same variables to one side, such as: 3x + 7x + 8x. Now, we only deal with these for now. You can ignore the variables for now, but add them later on the answer. So, 3 + 7 + 8 = 18, so the answer is 18x. Secondly, we put 18 x to our equation in the form of 18x + 3 - 6, Now, we deal with the other numbers without variables. so 18x + 3 - 6 = 18x + -3. So this is our answer!

      Also, I'm sure that you are not stupid and too slow to catch up with somebody else, somebody stupid would not have asked for help at all. You can do anything that you set your mind to, just make sure to focus on it. If you have to watch it over and over again, just remember that this is part of your learning stage as a student. It does not matter if you are slower that anybody else, you are learning at your pace, and you can do it. I hope I was not much of a bother and that this helped!
      (2 votes)
  • blobby purple style avatar for user Lillian A.
    What is a Chuck Norris
    (5 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Ja'on
    i don't have a question but dang there are comments from 9 years ago
    (5 votes)
    Default Khan Academy avatar avatar for user

Video transcript

Let's say that I've got 2 Chuck Norrises, or maybe it's Chuck Norri. And to that I am going to add another 3 Chuck Norrises. So I'm going to add another 3 Chuck Norrises. And this might seem a little bit obvious, but how many Chuck Norrises do I now have? Well, 2 Chuck Norrises, we can represent this as literally a Chuck Norris plus a Chuck Norris. So let me do that, a Chuck Norris plus another Chuck Norris, 2 Chuck Norrises. You could also do this 2 times Chuck Norris, and this is just another way of representing it. And 3 Chuck Norrises-- you could do that as a Chuck Norris plus a Chuck Norris plus another Chuck Norris. And so we would have a grand total-- and this might be very simple for you. But you would have a grand total of 1, 2, 3, 4, 5 Chuck Norrises. So this would be equal to 5 Chuck Norrises. Now, let's get a little bit more abstract here. Chuck Norris is a very tangible thing. So let's go to a little bit more of traditional algebraic notation. If I have 2x's and remember, you could do this as 2x's or 2 times x. And to that, I would add 3x's How many x's do I have? Well, once again, 2x's, that's 2 times x. You could do that as an x plus an x. We don't know what the value of x is. But whatever that value is, we can add it to itself. And then 3x's are they're going to be that value. Let me do that in that same green color. 3x's are going to be that value plus that value plus whatever that value is. And so how many x's do I now have? Well, I'm going to have 1, 2, 3, 4, 5 x's. So 2x plus 3x is equal to 5x. And if you think about it, all we really did-- and hopefully, you conceptually get it-- is we just added the 2 numbers that were multiplying the x. And these numbers, the 2 or the 3, they're called coefficients. Very fancy word, but it's just this constant number, this regular number that's multiplied by the variable. You just added the 2 and the 3, to get your 5x. Now, let's think about this a little bit more. Let's go back to this original expression, the 2 Chuck Norrises plus 3 Chuck Norrises. Let's say, to that, we were to add to some type of a-- let's we were to add 7 plums over here. So this is my drawing of a plum. So we have 7 plums plus 2 Chuck Norrises plus 3 Chuck Norrises. And let's say that I add another 2 plums. I add another 2 plums here. So what this whole thing be? Well, I wouldn't add the 7 to the 2 to the 3 plus the 2. We're adding different things here. You have 2 Chuck Norrises and 3 Chuck Norrises, so they're still going to simplify to 5 Chuck Norrises. . And then we would separately think about the plums. We have 7 plums, and we're adding another 2 plums. We're going to have 9 plums. Plus 9 plums, so this simplifies to five Chuck Norrises and 9 plums. Similarly, over here, instead of just 2x plus 3x, if I had 7y plus 2x plus 3x plus 2y, what do I now have? Well, I can't add the x's and the y's. They could very well represent a different number. So all I can do is really add the x's. And then I get the 5x. And then, I'd separately add the y. If I have 7y's and to that I add 2y's, I'm going to have 9y's. If I have 7 of something and I add 2 of something, I now have 9 of that something. So I'm going to have 9y's. So you add that. Do that in a different color. You add this and this. You get that. You add the x's. You get that right over there. So hopefully, that makes a little sense. Actually I'll throw out one more idea. So given this, what would happen if I were to have 2x plus 1 plus 7x plus 5? Well, once again, you might be tempted to add the 2 plus the 1, but they're adding different things. These are 2x's. This is just the number 1. So you really just have to add the x's together. So you're going to say, well, I got 2x's. And I'm going to add 7x's to that. Well, that means I now have 9x's. And then, separately, you'd say, well, I've got just the abstract number 1. And then I've got another 5. 1 plus 5 is going to be equal to 6.