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Adding and subtracting polynomials review

Adding and subtracting polynomials is all about combining like terms. In this article, we review some examples and give you a chance for you to practice the skill yourself.
Adding and subtracting polynomials is an exercise in combining like terms. Let's walk through some examples.

Example 1

Simplify.
left parenthesis, 5, h, cubed, minus, 8, h, right parenthesis, plus, left parenthesis, minus, 2, h, cubed, minus, h, squared, minus, 2, h, right parenthesis
Rewrite without parentheses:
start color #11accd, 5, h, cubed, minus, 8, h, end color #11accd, start color #ca337c, minus, 2, h, cubed, minus, h, squared, minus, 2, h, end color #ca337c
Group like terms:
left parenthesis, start color #11accd, 5, h, cubed, end color #11accd, start color #ca337c, minus, 2, h, cubed, end color #ca337c, right parenthesis, start color #ca337c, minus, h, squared, end color #ca337c, plus, left parenthesis, start color #11accd, minus, 8, h, end color #11accd, start color #ca337c, minus, 2, h, end color #ca337c, right parenthesis
Simplify:
3, h, cubed, minus, h, squared, minus, 10, h
Want to see another example? Check out this video.

Example 2

Simplify.
left parenthesis, minus, w, cubed, plus, 8, w, squared, minus, 3, w, right parenthesis, minus, left parenthesis, 4, w, squared, plus, 5, w, minus, 7, right parenthesis
Rewrite without parentheses (being careful to distribute the negative):
start color #11accd, minus, w, cubed, plus, 8, w, squared, minus, 3, w, end color #11accd, start color #ca337c, minus, 4, w, squared, minus, 5, w, plus, 7, end color #ca337c
Group like terms:
start color #11accd, minus, w, cubed, end color #11accd, plus, left parenthesis, start color #11accd, 8, w, squared, end color #11accd, start color #ca337c, minus, 4, w, squared, end color #ca337c, right parenthesis, plus, left parenthesis, start color #11accd, minus, 3, w, end color #11accd, start color #ca337c, minus, 5, w, end color #ca337c, right parenthesis, start color #ca337c, plus, 7, end color #ca337c
Simplify:
minus, w, cubed, plus, 4, w, squared, minus, 8, w, plus, 7
Want to see another example? Check out this video.

Example 3

Express E, plus, F as a trinomial.
E=6c22c1F=4c2+7c+5\begin{aligned} E &= 6c^2-2c-1 \\\\ F &= -4c^2+7c+5 \end{aligned}
E, plus, F, equals, left parenthesis, 6, c, squared, minus, 2, c, minus, 1, right parenthesis, plus, left parenthesis, minus, 4, c, squared, plus, 7, c, plus, 5, right parenthesis
Rewrite without parentheses and color code like terms:
start color #11accd, 6, c, squared, end color #11accd, start color #1fab54, minus, 2, c, end color #1fab54, start color #7854ab, minus, 1, end color #7854ab, start color #11accd, minus, 4, c, squared, end color #11accd, start color #1fab54, plus, 7, c, end color #1fab54, start color #7854ab, plus, 5, end color #7854ab
Group like terms:
start color #6495ed, left parenthesis, 6, minus, 4, right parenthesis, c, squared, end color #6495ed, plus, start color #28ae7b, left parenthesis, minus, 2, plus, 7, right parenthesis, c, end color #28ae7b, plus, start color #9d38bd, left parenthesis, minus, 1, plus, 5, right parenthesis, end color #9d38bd
Simplify:
2, c, squared, plus, 5, c, plus, 4
Want to see another example? Check out this video.

Practice

Problem 1
Simplify.
left parenthesis, minus, 3, y, squared, minus, 5, y, minus, 2, right parenthesis, plus, left parenthesis, minus, 7, y, squared, plus, 5, y, plus, 2, right parenthesis

Want more practice? Check out these exercises:

Want to join the conversation?

  • aqualine sapling style avatar for user mcallisterjrrandy
    I always forget to put the negative sign in front of the number if there is one and i get it wrong cause of that
    (5 votes)
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  • blobby green style avatar for user 2268ratz
    why is it important to learn polynomials?
    (12 votes)
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  • blobby green style avatar for user emmanuella.otu
    why does some of the exercises keep telling me to start over, when i have done it up to two to three times?
    (5 votes)
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    • duskpin ultimate style avatar for user Silver
      Maybe you did made three out of four or something like that but the exercises want you to learn how to solve the problem and when you get four of four question, then you are good to go! But When you make to Quiz and if you fail to pass Quiz... the exercises will rank down and make you come back to exercise that want you solve the problem to understand how it work.
      (4 votes)
  • mr pants pink style avatar for user nyrielcharley
    How wouldn't it be -10y with the exponent of 2 if all the other numbers cncel out
    (2 votes)
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  • male robot hal style avatar for user frost fzz
    for (3x+1)-(2x+3)
    we do 3x+1-2x-3 like -1(2x+3)
    is there video on khan academy explaining what's the fundamental behind this.
    (3 votes)
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    • stelly blue style avatar for user Kim Seidel
      with -(2x+3), you can distribute the "-" itself: -(2x) -(+3) which basically says change all terms to their opposite sign, and creates -2x-3

      Or, you can treat the "-" as -1. Remember "-x" is the same as "-1x". So, by changing the "-" to "-1", you are essentially doing the same thing.
      -1(2x+3) = -1(2x) -1(+3) = -2x-3

      You get the same result using either approach.
      Hope this helps.
      (5 votes)
  • primosaur seed style avatar for user sohia  paul
    What method can I use to remember to put in my negative n positive sign ,
    I’m having a little trouble with negative n positive.
    (4 votes)
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    • duskpin ultimate style avatar for user Victor
      - * - = +
      - * + = -
      + * + = +
      That's for multiplication rules. - * + is equal to + * -
      As for addition and subtraction, whichever sign's number is larger, they will take that sign.
      Example: -2 - (- 2) = -2 + 2 = 0
      I hope this helped!
      (2 votes)
  • leafers ultimate style avatar for user Alex
    Sometimes in subtracting polynomials I just dont know when to put like a - or a +
    (2 votes)
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  • blobby green style avatar for user Dryzta ovince
    do you guys have an easier method for this lesson?
    (4 votes)
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    • stelly blue style avatar for user Kim Seidel
      You may be over thinking this.
      Adding polynomials is the same as combining like terms. If you can combine like terms, then you can add polynomials.

      To subtract polynomials, you just need to remember to distribute the "minus" sign to all the terms in the polynomial being subtracted. Once you've done the distribution, you are back to combining like terms.

      Hope this helps.
      (2 votes)
  • blobby green style avatar for user Dhanu
    I just saw that everybody is asking what are polynomials used for. I'll give you the perfect answer-
    This algebra and stuff you're learning right now will not be useful in your future but the marks you're gonna gain by this will build your future!
    Don't you think?
    (4 votes)
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  • leaf blue style avatar for user Hennessey Venom F5
    What are polynomials used for?
    (3 votes)
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    • blobby green style avatar for user Mina
      " Since polynomials are used to describe curves of various types, people use them in the real world to graph curves. For example, roller coaster designers may use polynomials to describe the curves in their rides. Combinations of polynomial functions are sometimes used in economics to do cost analyses, for example."

      Also, you might find this interesting "Engineering Careers. Aerospace engineers, chemical engineers, civil engineers, electrical engineers, environmental engineers, mechanical engineers and industrial engineers all need strong math skills. Their jobs require them to make calculations using polynomial expressions and operations."
      (2 votes)