Polynomials and Like Terms

Vocabulary

100

In an expression, the parts being added together or subtracted. Example: 4x + 3x + 3y + 7y

Term

200

Terms that contain the same variable(s) raised to the same exponent. These terms can be combined. Example: 3x + 9x or 7y + 3y

Like Terms

300

A mathematical phrase that contains numbers, operations, and/or variables (but no = sign). Example: 5x + 4y + 5 - 2x

Expression

400

To take an expression and make it easier to evaluate if it has common variables and constants

Simplify

500

A symbol, usually a letter of the alphabet, used to represent an unknown value.

Variable

600

a mathematical expression composed of variables, coefficients, and exponents where the only operations used are addition, subtraction, and multiplication,

polynomial

Combine Like Terms (Add)

100

8a + 15a + a + 9

24a + 9

200

5x + 35 + 3x + 2

8x + 37

300

32 + 12t + 16t + 8

28t + 40

400

3x²y + 4xy + 4xy + 6 

3x²y + 8xy + 6

500

7m + 6m⁴n³ + 3m + 4m⁴n³ 

10m + 10m⁴n³ 

600

2(x⁴ + 3x⁴)

8x⁴

Combine Like Terms (Add & Subtraction)

100

21b - 11b - 10 - 2b

8b - 10

200

12c - 6c - 30

6c - 30

300

5z + 55 - 26 - z

4z + 29

400

3 + 13x + 3x² - 5x - 2x²

x² + 8x + 3

500

8p + 3p³ + 13 - 4p² - 2 - 6p

3p³ - 4p² + 2p + 11

600

2(6x⁴ - 3x⁴)⁰

2

Combine (Distributive)

100

3(7x²)

21x²

200

2(x² + y)

2x² + 2y

300

3(2m³ + 2n)

6m³ + 6n

400

4(2x + 3xy)

8x + 12xy 

500

4x(2 + 3)

20x

600

2⁰(x⁴ + 3x⁴)

4x⁴

Like Terms or Not Like Terms

100

7x + 7

NOT Like Terms

7x + 7

200

3x + 15x

Like Terms

18x

300

3m⁵n³ + 9m⁵n³

Like Terms

12m⁵n³

400

15x³yz - 5x³yz

 Like Terms

10x³yz 

500

22r⁵s³t - 3r⁵s³t²

NOT Like Terms

22r⁵s³t - 3r⁵s³t²

600

What is most important to focus on when combining like terms?

variables and exponents match!

Riddles

100

What gets wetter and wetter as it dries?

a sponge or towel

200

Where does a polar bear keep his money?

a snowbank

300

What is a butterfly's favorite subject?

Mothematics

400

What did the zero say to the eight?

nice belt

500

What do you call a fake noodle?

An Im-patsa!

600

What do you call a bear with no teeth?

a gummy bear!