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

Subtracting polynomials: two variables (intro)

Sal simplifies (4x²y - 3xy + 25) - (9y²x + 7xy - 20). Created by Sal Khan and Monterey Institute for Technology and Education.

Want to join the conversation?

  • marcimus pink style avatar for user Audrea Tobias Parham
    I thought to the rule of subtraction for poly's is to take the opposite then add. I thought it should be +(-9)y.........
    (12 votes)
    Default Khan Academy avatar avatar for user
  • leaf green style avatar for user Shalini.mizzican
    IS 4x^2y - 10xy - 9y^2x + 45 also acceptable? ...... I just swopped two of the terms around.
    (7 votes)
    Default Khan Academy avatar avatar for user
    • piceratops tree style avatar for user Jonathan Wong
      Ideally, you'd write it in order of decreasing powers with the variable first in alphabetical order. Sadly, it gets more complicated with multiple variables and when you have different powers.
      Personally, I'd write it like you did: The x's are in order of decreasing power, and the y's highest power is after the one with y^1. Just personal preference really. I would never say it's wrong if you write it in a different order: it's just how you interpret your answer.

      Hope I helped!
      (15 votes)
  • winston baby style avatar for user Nikolaos Garske
    Why does he put his answers in that order?
    (8 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user ahmed hamid
    isn't negative 3 minus seven suppose to be negative 7 because the 7 is followed by a minus sign?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • male robot hal style avatar for user saeed cool
    in my answer i got -5x^2y-10xy+45
    i thought that because 4x^2y-9x^2y would equal -5x^2y
    but instead he counted them as two different like terms,
    why is that?
    (3 votes)
    Default Khan Academy avatar avatar for user
  • hopper cool style avatar for user Janzen Go
    At , why did Sal wrote a number 1 in between of the quantities? What is the purpose of that?
    (4x²y - 3xy + 25) - 1 (9y²x + 7xy - 20)
    (5 votes)
    Default Khan Academy avatar avatar for user
  • leaf green style avatar for user hassan300700
    what if the question is like 9xy - 12yx. what would u do here. would these be considered as LIKE TERMS
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user 18sren
    How do you write this in standard form for this? Which variable comes first?
    (2 votes)
    Default Khan Academy avatar avatar for user
    • leaf green style avatar for user jude4A
      The most common way is seen polynomials arranged is to have the highest power of the lowest letter of the variables go first and then arrange the remaining items in a "descending" order where the constant is the last item in the arrangement. You don't have to arrange it on any particular order. We can arrange them however we want due to the commutativity of addition. What really matters is that you can tell the difference between the terms and understand that objects like (x^2)(y) and (x)(y^2) are not necessarily the same thing. Hope this helps. Good luck!
      (5 votes)
  • blobby green style avatar for user Daniel Awe
    if you add x and x together does that make x^2
    (1 vote)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user 1000189
    I am confused. Like what would be the answer if you did x to the fourth power plus x to the 3rd power
    (3 votes)
    Default Khan Academy avatar avatar for user
    • duskpin ultimate style avatar for user Adriel
      You would be left with x^4 + x^3. You are unable to add different powers of the same variable. The order of operations states that exponents must be evaluated before addition, but since the exponent cannot be evaluated without knowing the value of x, the addition cannot be done either.
      (1 vote)

Video transcript

We've got 4x squared y minus 3xy plus 25 minus the entire expression 9y squared x plus 7xy minus 20. So when we're subtracting this entire expression, that's equivalent to subtracting each of these terms individually if we didn't have the parentheses. Or another way of thinking about it-- we could distribute this negative sign. Or you could view this as a negative 1 times this entire expression. And we can distribute it. So let's do that. So let me write this first expression here. I'm going to write it unchanged. So it is 4x squared y minus 3xy plus 25. And now let me distribute the negative 1, or the negative sign times all of this stuff. So negative 1 times 9y squared x is negative 9y squared x. Negative 1 times 7xy is negative 7xy. And then negative 1 times 20 is positive 20. And now we just have to add these terms. And we just want to group like terms. So let's see, is there another x squared y term anywhere? No, I don't see one. So I'll just rewrite this. So we have 4x squared y. Now, is there another xy term? Yeah, there is. So we can group negative 3xy and negative 7xy. Negative 3 of something minus another 7 of that something is going to be negative 10 of that something. So it's negative 10xy. And then we have a 25, which is just a constant term. Or an x to the 0 term. It's 25x to the 0. You could view it that way. And there's another constant term right over here. We can always add 25 to 20. That gives us 45. And then we have this term right over here, which clearly can't be merged with anything else. So minus 9y squared. Let me do that in that original color. Minus 9-- I'm having trouble shifting colors-- minus 9y squared x. And we are done.