1. Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes

2. Warm Up
Simplify.
 5 + 3 20
2. 16   1 11  8
 20  2 3

3. Problem of the Day
Ray and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see?
7 turkeys, 8 deer

4. Learn to combine like terms in an expression.

5. Vocabulary
terms
like terms
equivalent expressions
simplify

6. Terms in an expression are separated by plus or minus signs.
Like terms can be grouped together because they have the same variable raised to the same exponents.
Constants such as 4, 0.75, and 11 are like terms because none of them have a variable.
Helpful Hint
Equivalent expressions have the same value for all values of the variables.

7. To simplify an expression, perform all possible operations, including combining like terms.

8. Additional Example 1: Combining Like Terms To Simplify
Combine like terms.
A. 14a – 5a
Identify like terms. 9a
Combine coefficients: 14 – 5 = 9
Identify like terms; the coefficient of y is 1, because 1y = y.
B. 7y2 + 8 – 3y2 – 1 + y
Combine coefficients: 7 – 3 = 4 and 8 – 1 = 7
4y2 + y + 7

9. Additional Example 2A: Combining Like Terms in Two-Variables Expressions
Combine like terms.
5t2 + 7p – 3p – 2t2
5t2 + 7p – 3p – 2t2
Identify like terms.
3t2 + 4p
Combine coefficients.

10. Additional Example 2B: Combining Like Terms in Two-Variable Expressions
Combine like terms.
4m3 + 9n – 2
4m3 + 9n – 2
No like terms.

11. The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5).
Remember!

12. Additional Example 3: Using the Distributive Property to Simplify
Simplify 6(5 + n) – 2n.
6(5 + n) – 2n
6(5) + 6(n) – 2n
Distributive Property.
30 + 6n – 2n
Multiply.
30 + 4n
Combine coefficients: 6 – 2 = 4.

13. Additional Example 4: Combining Like Terms to Solve Algebraic Equations
Solve x + 3x = 48.
x + 3x = 48
Identify like terms. The coefficient of x is 1.
4x = 48
Combine coefficients: = 4
4x = 48
Divide both sides by 4. 4 4
x = 12

14. Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems

15. Lesson Quiz Combine like terms.
1. 3x x k + 6 – 8m k
Simplify.
3. 4(3x + 6) – 7x (x + 5) + 3x
Solve.
5. 6y + y = 42
6. The Accounting Department ordered 15 boxes of pens. The Marketing Department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens?
5x2 + 4
14k – 8m + 15
5x + 24
9x + 30
y = 6 $3

16. Lesson Quiz for Student Response Systems
1. Combine like terms.
4p p
A. 15p2 + 13
B. 15p + 13
C. 28p
D. 28

17. Lesson Quiz for Student Response Systems
2. Combine like terms.
15t + 9 – 7s t
A. 15t – 7s – 1
B. 15t – 7s + 1
C. 20t – 7s + 19
D. 20t + 7s + 19

18. Lesson Quiz for Student Response Systems
3. Simplify 7(4m + 9) – 9m.
A. 19m + 9
B. 19m + 63
C. 37m + 9
D. 37m + 63

19. Lesson Quiz for Student Response Systems
4. Solve 11v + 2v = 65.
A. v = 2
B. v = 5
C. v = 7
D. v = 11