Simplifying Expressions

Combining Like Terms

100

2y + 3y

5y

200

3x + 5 + 6x

9x + 5

300

x + x + x + x

4x

400

8m + 2y - 3m + 10y + 4

5m + 12y + 4

500

22xy + 9x + 5y - x - y - 6xy + x

16xy + 9x + 4y

Distributive Property

100

2 (x + 5)

2x + 10

200

5 (m - 3)

5m - 15

300

3 (x + y + 4)

3x + 3y + 12

400

8 (2x - 4)

16x - 32

500

3 ( 2m + 4x - 5y)

6m + 12x - 15y

Combining Like Terms & Distributive Property

100

2(x + 5) + 3

2x + 10 + 3 = 2x + 13

200

8 + 4(x - 1)

8 + 4x - 4 = 4 + 4x

300

2y + 4(y + 3) 

2y + 4y + 12 = 6y + 12

400

3x + 4 + 5(2x + 3)

3x + 4 + 10x + 15 = 13x + 19

500

23xy + 4x + 2(2xy + 3x) - xy

23xy + 4x + 4xy + 6x - xy = 

26xy + 10x

Misc.

100

How many terms are in this expression:

6x + 9 - 12y + 10

4

200

In the term 5y, what operation is going on between the 5 and the y?

multiplication

300

What is the coefficient of x if there is no number written in front of it?

1

400

In the expression 5m + 8, what do we call the term "8"? (What vocab word)

Constant

500

Look at the following expression:
4x+3y+7x-2y+5

Which terms can be combined because they are like terms, and which terms should remain separate?

Like terms have the same variable raised to the same power. In this expression:

• 4x and 7x are like terms because they both have the variable x.
• 3y and −2y are like terms because they both have the variable y.
• The constant 5 has no variable, so it stands alone.

So, 4x and 7x can be combined, and 3y and −2y can be combined.

Factoring

100

Find the GCF between 4 and 18

2

200

Find the GCF between 8 and 32

8

300

Factor the following expression: 12x + 16

4(3x + 4) 

400

Factor the following expression: 5x+22

Cannot be factored

500

Factor the following expression: 45x−90y

45(x-2y)