1. Exercise Find the following products mentally. 5(20) 100 5(7) 35 5(27)
135

2. Exercise Find the following products mentally. 3(20) 60 3(3) 9 3(23)69

3. Exercise
Find the following products mentally.
7(82)
574

4. Distributive Property
For any integers a, b, and c, a(b + c) = ab + ac.

5. Example
3(2 + 5) = 3 • • 5
3(7) =
21 = 21

6. a(b – c) = ab – ac

7. Example
3(8 − 5) = 3 • 8 − 3 • 5
3(3) = 24 − 15
9 = 9

8. Example 1
Use the Distributive Property to write an equivalent expression. Then simplify if possible.
−5(2 − 7) =
−5 • 2 − (−5) • 7
= −10 − (−35)
= −
= 25

9. Example 1
Use the Distributive Property to write an equivalent expression. Then simplify if possible.
4(m + n) =
4m + 4n

10. 3(74)

11. ab + ac = a(b + c)

12. Example 2
Use the Distributive Property to write an equivalent expression.
4(−8) + 4(32) =
4(−8 + 32)

13. Example 2
Use the Distributive Property to write an equivalent expression.
−3(7) − 3x =
−3(7) + (−3)x
= −3(7 + x)

14. Example 3 Write an equivalent expression for (5 + x)y. (5 + x)y =

15. Exercise
Identify the property used for each step in simplifying the following.
6 + 3r + 5 =
= 3r
= 3r + 11

16. Exercise
Identify the property used for each step in simplifying the following.
4n + 2m + 9n =
= 4n + 9n + 2m
= (4 + 9)n + 2m
= 13n + 2m

17. Exercise
Identify the property used for each step in simplifying the following.
2x + 3y − 4x + 8 =
= 2x − 4x + 3y + 8
= (2 − 4)x + 3y + 8
= −2x + 3y + 8

18. Exercise
Identify the property used for each step in simplifying the following.
2(h + 3) + h =
= 2h + h + 6
= 2h + 1h + 6
= (2 + 1)h + 6
= 3h + 6

19. Exercise
Identify the property used for each step in simplifying the following.
(5b + 6) − 2b =
(6 + 5b) − 2b
= 6 + (5b − 2b)
= 6 + (5 − 2)b
= 6 + 3b
= 3b + 6