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

Adding polynomials

Learn how to simplify polynomials by combining like terms! Discover the power of adding and subtracting terms with the same degree of x. Uncover the magic of removing parentheses and grouping similar terms together to simplify complex expressions. Master the art of polynomial simplification! Created by Sal Khan and Monterey Institute for Technology and Education.

Want to join the conversation?

  • blobby green style avatar for user Madhumitha Rangaraj
    At , Sal says that you can get rid of the parentheses. According to PEMDAS don't you have to complete everything inside of the parentheses before you move on? Why is it okay to ignore the parentheses?
    (16 votes)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user Janiya Fu
    I don't get why -5t - 3t equals -8t on my textbook, if the subtraction sign also applies to 3t as a negative sign, wouldn't the answer be -2t because you have to change the subtrahend every time, -3t turns into 3t, then you subtract, it becomes -2t. I don't really get it.
    (3 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Sacia Ashe
    Why do you have to distribute a negative?
    (6 votes)
    Default Khan Academy avatar avatar for user
  • old spice man green style avatar for user hyah21
    Is the process the same when you are subtracting?
    (7 votes)
    Default Khan Academy avatar avatar for user
  • old spice man blue style avatar for user angper23
    how would you combine the terms if they had different exponents
    (6 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user Victor
      In that case, you wouldn't be able to combine the terms. Could you give me an example so that I could walk you through it? Some scenarios will allow you to add different exponents (after distribution)
      (9 votes)
  • female robot grace style avatar for user sarra
    this seems fun
    (7 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user dbutcher28
    Isnt that equation 2 trinomials?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • starky sapling style avatar for user Sean Sherwin
    Bro what is this fr I’m so confused
    (3 votes)
    Default Khan Academy avatar avatar for user
    • hopper cool style avatar for user EducatedUser4Khan
      This may help
      The given expression is: (5x² + 8x - 3) + (2x² - 7x + 13x)

      First, let's combine the like terms within each set of parentheses:

      In the first set of parentheses, we have: 5x² + 8x - 3

      In the second set of parentheses, we have: 2x² - 7x + 13x

      Now, let's combine the like terms within each set:

      For the first set, there are no like terms to combine.

      For the second set, the like terms are: -7x and 13x, which combine to give 6x.

      Now, we have:

      5x² + 8x - 3 + 2x² + 6x

      Next, let's combine the like terms across both sets:

      5x² + 2x² = 7x²

      8x + 6x = 14x

      Putting it all together, the simplified form of the expression is:

      7x² + 14x - 3
      (5 votes)
  • male robot hal style avatar for user Bork Doggo
    me looking at these questions that were commented years ago and the nostalgia comes of doing khan academy
    (5 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user vapsy36198
    Add the polynomial functions: \large f\left(x\right)=4x^2+3x-5

    and \large g\left(x\right)=2x^2-x+1.

    Combine the like terms and type in your answer in equation form by clicking on the "Insert Content" with an arrow and select "Equation".
    (3 votes)
    Default Khan Academy avatar avatar for user
    • female robot grace style avatar for user loumast17
      You should keep it neater, so get rid of the coding type text. just have f(x) = 4x^2 + 3x - 5 and g(x) = 2x^2 - x + 1

      Since you are adding the polynomials you have 4x^2 + 3x - 5 + 2x^2 - x + 1.

      To add them you do exactly as the instructions say, combine like terms. This just means look for matching variables. For instance 5x^4 - 6x^4 would be like terms since they have x^4. Combining like terms just means to do what the math says to the coefficients. so 5x^4 - 6x^4 means take 5 - 6 since the two are being subtracted. so 5x^4 - 6x^4 = -1x^4 or just -x^4

      The three kinds of terms are those that have x^2, x and no variable at all. I will get you started, the non variable terms are -5 and + 1 so combining the gets you -4. can you take it from there?

      I will give a different example to further help.

      x^4 - 7x^3 + 3 - 5x^4 + 8x^3 + 3
      here are the like terms
      x^4 - 5x^4 = -4x^4
      -7x^3 +8x^3 = x^3
      3 + 3 = 6

      So now you have -4x^4 + x^3 + 6

      Let me know if yous till don't understand
      (5 votes)

Video transcript

We're asked to simplify 5x squared plus 8x minus 3 plus 2x squared minus 7x plus 13x. So really, all we have to do is we have to combine like terms-- terms that have x raised to the same power. And the first thing we can do, we can actually get rid of these parentheses right here, because we have this whole expression, and then we're adding it to this whole expression. The parentheses really don't change our order of operations here. So let me just rewrite it once without the parentheses. So we have 5x squared plus 8x minus 3 plus 2x squared. If this was a minus then we'd have to distribute the negative sign, but it's not. So plus 2x squared minus 7x plus 13x. Now let's just look at the different terms that have different degrees of x. Let's start with the x squared terms. So you have a 5x squared term here and you have a 2x squared term right there. So 5 of something plus 2 of that same something is going to be 7 of that something. So that's going to be 7x squared. And then let's look at the x terms here. So we have an 8x right there. We have a minus 7x. And then we have a plus 13x. So if you have 8 of something minus 7 of something, you're just going to have 1 of that something. And then if you add 14 of that something more, you're going to 15. So this is going to be plus 15x. 8x minus 7x-- oh, sorry. You're going to have 14x. 8 minus 7 is 1 plus 13 is 14. Plus 14x. That's these three terms. 8x minus 7x plus 13x. And then finally, you have a negative 3-- or minus 3, depending on how you want to view it. And that's the only constant term. You could say it's x times x to the 0. But it's a constant term. It's not be multiplied by x. And that's the only one there, so minus 3. And we've simplified it as far as we can go. We are done.