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: Algebra 2>Unit 1

Lesson 3: 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:

## Want to join the conversation?

• What are polynomials used for?
• " 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."
• 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
• same
• Who is ready for the new academic year?? lets start off this year strong guys!
• Not me... I don like school... 😔
• why is it important to learn polynomials?
• It is actually used in a lot of careers in the future, like engineering, finance, or other math-related fields.
• This is better than Kumon I must admit
• yes, you're right
• im stressed
• me too
• why am i doing this?
• to learn or review
• this class is kind of easy and hard
• 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.