Here are the steps to find the perimeter of the figure: 1) Side 1 = 5 units 2) Side 2 = 8 units 3) Side 3 = 5 units 4) Side 4 = 8 units 5) Perimeter = Side 1 + Side 2 + Side 3 + Side 4 = 5 + 8 + 5 + 8 = 26 The expression for the perimeter is: 5 + 8 + 5 + 8 Combining like terms gives: 26 Therefore, the expression for the perimeter of the figure, combining like terms, is 26 units.

1. Name ___________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 7 Combining Like Terms
OC 3-5
Essential Question: How can using properties help you to represent mathematical relationships?
Vocabulary Definition Example
Like Terms
Equivalent expression
Let’s Review:
Look at the following expressions:
x = 1x
x + x = 2x
x + x + x = 3x
The numbers 1, 2, and 3 are called coefficients of x.
An algebraic expression has terms that are separated by + and -.
In the expression 2x + 5y, the terms are 2x and 5y.
Sometimes the terms of an expression can be combined. Only like terms can be combined.
7w + w like terms
2x - 2y + 2 unlike terms because x and y are different variables
8e - 3e + 2e like terms
5d + 25g unlike terms because d and g are different variables
To simplify an expression:
Step 1: Combine like terms.
Step 2: Add or subtract the coefficients of the variable.
7w + w = 8w

2. Identify and underline like terms.
1. 6a b a 17 4b 32 17a 2. x x2 3x 3 3x2 6
______________________________________
____________________________________
3. 2 6z 6z2 z 17z z2 3 4. m 8 8m2 8m m2 12m 18
______________________________________
____________________________________
5. The terms y and 2y3 contain the same variable but are not like terms. Why not?
__________________________________________________________________________
Combine like terms.
6. 6p2 + 3p2 7. 9x - 6x
8. a2 + b2 + 2a2 + 5b2 9. 7h2 + 3 - 2h2 + 4
10. 3x + 3y + x + y + z 11. 5b + 5b + 6b2 – 10 - 3b
12. Find the perimeter of the rectangle.
Combine like terms.

3. Name ___________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 7 Combining Like Terms
OC 3-5
Essential Question: How can using properties help you to represent mathematical relationships?
Vocabulary Definition Example
Terms with the same 12 + 3y3 + 4x + 2y3
Like Terms variable(s) raised to the 3y3 and 2y3
same power(s) are like terms
Expressions that
simplifying to the same
Equivalent expression value for any y + y + y = 3y
number(s) substituted
for the variable(s)
Let’s Review:
Look at the following expressions:
x = 1x
x + x = 2x
x + x + x = 3x
The numbers 1, 2, and 3 are called coefficients of x.
An algebraic expression has terms that are separated by + and -.
In the expression 2x + 5y, the terms are 2x and 5y.
Sometimes the terms of an expression can be combined. Only like terms can be combined.
7w + w like terms
2x - 2y + 2 unlike terms because x and y are different variables
8e - 3e + 2e like terms
5d + 25g unlike terms because d and g are different variables
To simplify an expression:
Step 1: Combine like terms.

4. Step 2: Add or subtract the coefficients of the variable.
7w + w = 8w
The terms y and 2y3 contain the same variable but are not like terms. Why not?
The variable is not raised to the same power.

5. Name ___________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 7 Combining Like Terms HW
OC 3-5
Identify like terms.
1. 3a b 2 b3 4b2 4 5a
____________________________________
2. x x4 4x 4x2 4x4 3x2 ____________________________________
3. 6m 6m2 n2 2n2 4m 5n
____________________________________
4. 12s 7s4 9s s2 5 5s4
2___________________________________
Combine like terms.
5. 2p + 22q2 - p 6. x2 + 3x2 - 42
7. n4 + n3 + 3n – n - n3 8. 4a + 4b + 2 - 2a + 5b – 1
9. 32m2 + 14n2 - 12m2 + 5n - 3 10. 2h2 + 3g - 2h2 + 22 - 3 + 4g
11. Write an expression for the perimeter of the
figure at right. Combine like terms in the expression.

6. Name ___________________________________ Date _________________________
Mrs. Labuski / Mrs. Portsmore Period _____ Unit 4 Lesson 7 Combining Like Terms HW
OC 3-5