1. Unit 3. Day 1.

2. Please get out paper for today’s lesson
Name
Date
Period
Topic: Combining Like Terms & Distributive Property
Use properties of operations to generate equivalent expressions

3. Combine
“Like Terms”

4. Q: What are terms? 3𝑥−2 2 terms 3𝑥−8𝑦+5 3 terms 4 𝑚 3 −7 𝑛 2 +11𝑝−4
6 𝑎 2 𝑏 𝑐 99 𝑑
1 term

5. Combine “Like Terms” 4 + + 2 + 3 + 1 5

6. Example A:
4𝑥+3+2𝑥+2 6𝑥
+ 5
4𝑥+3+2𝑥+2 4𝑥
+ 3
+ 2𝑥
+ 2 6𝑥
+ 5
We have simplified the expression by “combining like terms”
Using the commutative property of addition

7. −4𝑥−3+2𝑥−2 −2𝑥 − 5 −4𝑥 −4𝑥 + −3 + −3 − 3 + 2𝑥 + 2𝑥 + −2 + −2 − 2 −2𝑥
Example B:
−4𝑥−3+2𝑥−2
−2𝑥
− 5
−4𝑥
−4𝑥
+ −3
+ −3
− 3
+ 2𝑥
+ 2𝑥
+ −2
+ −2
− 2
−2𝑥
− 5
We have simplified the expression by “combining like terms”
Using the commutative property of addition

8. Example C*:
7𝑛+10−5+11𝑛+2−8𝑛
Example D*:
12𝑚−3𝑡+2−8𝑚+ −7 −𝑡−2𝑚

9. Example C*:
7𝑛+10−5+11𝑛+2−8𝑛
10𝑛
+ 7

10. Example D*:
12𝑚−3𝑡+2−8𝑚+ −7 −𝑡−2𝑚 2𝑚 2𝑚
−4𝑡
−4𝑡 −5 −5 +

11. − 1 2 𝑥− 3 4 + 3 8 𝑥+ 1 4 −0.6𝑥+ −2.3𝑦 +0.25𝑥−3.2+5.55𝑦 Example F*:
− 1 2 𝑥− 𝑥+ 1 4
Example F*:
Example G*:
−0.6𝑥+ −2.3𝑦 +0.25𝑥− 𝑦

12. − 1 2 𝑥− 3 4 + 3 8 𝑥+ 1 4 − 1 8 𝑥 − 1 2 Example F*: − 1 2 + 3 8
− 1 2 𝑥− 𝑥+ 1 4
− 1 8 𝑥
− 1 2 − − 4 3
− 1 8 − −2 4
− 1 2 = = = =

13. −0.35𝑥 + 3.25𝑦 − 3.2 −0.6𝑥+ −2.3𝑦 +0.25𝑥−3.2+5.55𝑦 Example G*: 0 . 6 01 − − . 3 5 3 . 2 5

15. Distributive Property

16. Example H: Use the Distributive Property
6(𝑦−7) 6𝑦 +
−42

17. Example I*: Use the Distributive Property
−4(3𝑥+7)
−12𝑥 +
−28

18. Example J: Use the Distributive Property
− (5−3𝑚) 1 −5 +
+3𝑚

19. Example K: Simplify
5(𝑥 + 3) −7𝑥 + 2
−7𝑥 + 2 5𝑥
+ 15
−2𝑥
+ 17

20. Simplify
− 8−3𝑛 +9+𝑛
Example L*:
6− 8−3𝑛 +9+𝑛
Example M*:

21. Example L*:
− 8−3𝑛 +9+𝑛
+ 9+𝑛 1 −8
+ 3𝑛 1 1
+ 4𝑛 4𝑛 +

22. Example M*:
6− 8−3𝑛 +9+𝑛 6
+ 9+𝑛 1 −8
+ 3𝑛 7
+ 4𝑛