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.

### Course: Get ready for Precalculus>Unit 2

Lesson 1: Adding and subtracting polynomials

# 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.
$\left(5{h}^{3}-8h\right)+\left(-2{h}^{3}-{h}^{2}-2h\right)$
Rewrite without parentheses:
$5{h}^{3}-8h-2{h}^{3}-{h}^{2}-2h$
Group like terms:
$\left(5{h}^{3}-2{h}^{3}\right)-{h}^{2}+\left(-8h-2h\right)$
Simplify:
$3{h}^{3}-{h}^{2}-10h$
Want to see another example? Check out this video.

### Example 2

Simplify.
$\left(-{w}^{3}+8{w}^{2}-3w\right)-\left(4{w}^{2}+5w-7\right)$
Rewrite without parentheses (being careful to distribute the negative):
$-{w}^{3}+8{w}^{2}-3w-4{w}^{2}-5w+7$
Group like terms:
$-{w}^{3}+\left(8{w}^{2}-4{w}^{2}\right)+\left(-3w-5w\right)+7$
Simplify:
$-{w}^{3}+4{w}^{2}-8w+7$
Want to see another example? Check out this video.

### Example 3

Express $E+F$ as a trinomial.
$\begin{array}{rl}E& =6{c}^{2}-2c-1\\ \\ F& =-4{c}^{2}+7c+5\end{array}$
$E+F=\left(6{c}^{2}-2c-1\right)+\left(-4{c}^{2}+7c+5\right)$
Rewrite without parentheses and color code like terms:
$6{c}^{2}-2c-1-4{c}^{2}+7c+5$
Group like terms:
$\left(6-4\right){c}^{2}+\left(-2+7\right)c+\left(-1+5\right)$
Simplify:
$2{c}^{2}+5c+4$
Want to see another example? Check out this video.

## Practice

Problem 1
Simplify.
$\left(-3{y}^{2}-5y-2\right)+\left(-7{y}^{2}+5y+2\right)$

Want more practice? Check out these exercises: