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

Adding like terms is a fundamental concept in algebra. Coefficients are the numbers in front of variables, and they can be added when the variables are the same. For example, 2x + 3x equals 5x. When dealing with different variables, such as x and y, add them separately, resulting in expressions like 5x + 9y. Created by Sal Khan.

Want to join the conversation?

  • blobby green style avatar for user ryant5185
    I get it but im lost on the operations. how do you know when to divide, subtract, add, or multiply?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • mr pink green style avatar for user David Severin
      If you are only combining like terms, stick to adding or subtracting. This depends on the coefficients, but we still use the laws of adding and subtracting positive and negative numbers. You would have to add multiply/divide only if you have to distribute something to everything in the parentheses such as 4(3x-4). Once you distribute, you get back to adding/subtracting.
      (8 votes)
  • leafers seedling style avatar for user EDiaz1786
    So are we basically just simplifying the answer?
    (3 votes)
    Default Khan Academy avatar avatar for user
    • starky ultimate style avatar for user ¿Mæstrø?J̊éđi
      @EDiaz1786

      Exactly right! You're pretty much simplifying the answer. A quick tip: If you see two numbers with the same variable and it tells you to add them... Add it! Below is an example of what I mean.

      3x + 4x = 7x

      In this case, you would only add the whole numbers and not multiply or add the x's, because if you added/multiplied the x's it would come out to be 7². But later on in Algebra 1, when you get to factoring and multiplying perfect squares that's when you'll multiply the x's AND the numbers. Here's a quick example of what I mean.

      7x(2x+4)

      This is saying that we distribute the 7x to the 2x and the 4. So the answer will be 14² + 28x.

      Hope this helps!
      (5 votes)
  • mr pants teal style avatar for user SiennaPitbull
    so am i adding the X's for my answer?
    (410 votes)
    Default Khan Academy avatar avatar for user
  • male robot donald style avatar for user panda
    this might seem kind of strange but when i was trying to figure out how to add like terms i stumbled upon the fact that adding like terms can be solved by doing the distributive property in reverse. i am not sure if this makes sense or not, but it made sense to me.

    for example:

    2X + 3X = X(2+3)= X(5) = 5X

    i do not like learning rules without understanding why the rules work. i know that you are suppose to simply add the coefficients of like terms and be done with the problem. but is that a shortcut/rule that was made instead of doing the distributive property in reverse ?
    (234 votes)
    Default Khan Academy avatar avatar for user
  • starky ultimate style avatar for user Finn
    Is zero prime, composite or neither?
    (98 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=?
    (37 votes)
    Default Khan Academy avatar avatar for user
  • mr pants green style avatar for user WilsonT
    The chuck norris part makes this video better
    (40 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!
    (14 votes)
    Default Khan Academy avatar avatar for user
    • aqualine ultimate style avatar for user Hannah Alisse
      When you're combining like terms, you're not actually solving for anything
      (It's not an equation if you don't have the equal sign)
      Combining like terms just means you add together anything you can.

      -n + (-3) +3n +5
      In your example, you have two types of numbers. You have numbers that are a multiple of n and you have regular numbers.

      The first thing I usually do is rearrange the numbers so that all the like terms or numbers that can be added together, are next to each other, like this:

      -n + 3n + (-3) +5

      Then you can rearrange it some more to make it clear how to combine the like terms

      3n-n + 5-3

      2n + 2

      Does that help?
      (31 votes)
  • blobby green style avatar for user 12604
    this is how u make math interesting
    (27 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user Geo.
    Is there a way to understand math better?
    (12 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.