Main content

## Algebra (all content)

### Unit 10: Lesson 2

Adding & subtracting polynomials- Adding polynomials
- Add polynomials (intro)
- Subtracting polynomials
- Subtract polynomials (intro)
- Polynomial subtraction
- Adding & subtracting multiple polynomials
- Add & subtract polynomials
- Adding polynomials (old)
- Adding and subtracting polynomials review

© 2022 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Adding polynomials

CCSS.Math: ,

Sal simplifies (5x² + 8x - 3) + (2x² - 7x + 13x). Created by Sal Khan and Monterey Institute for Technology and Education.

## 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.