Adding Polynomials

Simplifying Like Terms

Like terms are terms that have the same variables and same degrees!

Like Terms

A term is made up of 3 parts:
1. Coefficient
2. Variables
3. Degree/Exponents

Terms

Like Terms

In the image to the right, the left column contains like terms. They are like terms because they have the same variable with the same degree (x and x,
w and w, a² and a², etc.)

​

The right column has unlike terms. They are unlike because they either have different variables, or the variables have different exponents
(x and a, w and w²,
a² and a³, etc.)

​

YOUR TURN

Determine whether the following terms are like or unlike!

Multiple Choice

2x and 24x

• Like

• Unlike

Multiple Choice

7x and -3x

• Like

• Unlike

Multiple Choice

2a and 3b

• Like

• Unlike

Multiple Choice

2a and 3ab

• Like

• Unlike

Multiple Choice

5y and -y²

• Like

• Unlike

Multiple Choice

4d²e and -0.5d²e

• Like

• Unlike

Multiple Choice

-3x²y and 2xy²

• Like

• Unlike

Multiple Choice

-8a² and 3a²

• Like

• Unlike

Multiple Choice

2x² and 3

• Like

• Unlike

Multiple Choice

x and -6x

• Like

• Unlike

Simplifying Polynomials

Simplifying Polynomials

When simplifying polynomials, we are only able to combine like terms. We combine like terms by either adding or subtracting the coefficients.

For example

4x + 3x = 7x
5x + 3y + 4x + y + 5 = 9x + 4y + 5
7x² + 5x + 3 + 3x² + 4x + 5 = 10x² + 9x + 8

Note: Only the coefficient changes! The variables and degrees DO NOT CHANGE

Fill in the Blank

3x + 5x

Fill in the Blank

7a + 9a

Fill in the Blank

9m + 6m

Fill in the Blank

13x + 8x

Fill in the Blank

2y + 4y + 5y

Fill in the Blank

8y + y

Multiple Choice

3x + 4y + 2x + 5y

• 14xy

• 14x + 14y

• 7x + 7y

• 5x + 9y

Multiple Choice

6a + 2b + 3 + 4a + 5b

• 10a + 7b + 3

• 8ab + 9ba + 3

• 23ab

• 20ab + 3

Multiple Choice

4x² + 5x + 3 + 8x²

• 9x + 3 + 8x²

• 17x + 3

• 12x² + 5x + 3

• 17x² + 3

Multiple Choice

7x + 5x² + 9 + 8x

• 5x² + 14

• 5x² + 15x + 9

• 20x³ + 9

• 12x + 9 + 8x²

Open Ended

Reflect: What is something that you learned from today's lesson?

Poll

Reflect: How do you feel after today's lesson?

• I didn't get anything!

• I feel confused. I have questions.

• I feel so-so. I understood a few things.

• I get it. I am feeling good.

• I get it completely. I feel like an expert!