1. 1-4: The Distributive Property
Essential Skills:
Use the distributive property to evaluate expressions
Use the distributive property to simplify expressions

2. 1-4: The Distributive Property
For any numbers a, b, and c
a(b + c) = ab + ac and (b + c)a = ab + ac
a(b – c) = ab – ac and (b – c)a = ab – ac
Take the number outside the parenthesis and distribute (multiply) it with ALL the terms inside the parenthesis
Example
3(2 + 5) = 3 ● ● = = 21

3. 1-4: The Distributive Property
Julio walks 5 days a week. He walks at a fast rate for 7 minutes and cools down for 2 minutes. Use the Distributive Property to write and evaluate an expression that determines the total number of minutes Julio walks.
5 days of 7 minutes plus 2 minutes
5(7 + 2)
5 ● ● 2
45 minutes

4. 1) Rewrite 5(15 + 10). Then evaluate
● 10; 65
5 ● ; 85
5 ● ● 10; 125
; 25 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

5. 1-4: The Distributive Property
Mental Math
Use the Distributive Property to rewrite 12 ● 82. Then evaluate.
Think: 12 =
(10 + 2)(82)
10 ● ● 82
984

6. 2) Use the Distributive Property to rewrite 6 ● 54. Then evaluate
6(50); 300
6(50 ● 4); 1200
6(50 + 4); 324
6(50 + 4); 624 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

7. 1-4: The Distributive Property
Rewrite 12(y + 3) using the Distributive Property. Then simplify.
12(y + 3)
12 ● y + 12 ● 3
12y + 36

8. 1-4: The Distributive Property
Rewrite 4(y2 + 8y + 2) using the Distributive Property. Then simplify.
4(y2 + 8y + 2)
4 ● y2 + 4 ● 8y + 4 ● 2
4y2 + 32y + 8

9. 3) Simplify 6(x – 4) 6x – 4 6x – 24 x – 24 6x + 2 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

10. 4) Simplify 3(x3 + 2x2 – 5x + 7) 3x3 + 2x2 – 5x + 71 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

11. 1-4: The Distributive Property
The Distributive Property (in reverse) is how we can combine like terms
Simplify 17a + 21a
17a + 21a = ( )a = 38a
Simplify 12b2 – 8b2 + 6b
12b2 – 8b2 + 6b = (12 – 8)b2 + 6b = 4b2 + 6b

12. 5) Simplify 14x – 9x
5x2
23x 5 5x 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

13. 6) Simplify 6n2 + 7n + 8n 6n2 + 15n 21n2 6n2 + 56n 62n2 1 2 3 4 5 6 79 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

14. 1-4: The Distributive Property
Simplify the expression six times the sum of x and y increased by four times the difference of 5x and y.
Write verbal expression as an algebraic expression
6(x + y) + 4(5x – y)
Distribute
6x + 6y + 20x – 4y
Combine like terms
6x + 20x + 6y – 4y
(6 + 20)x + (6 – 4)y
26x + 2y

15. 7) Simplify the expression: three times the difference of 2x and y increased by two times the sum of 4x and y
2x + 4y
11x
14x – y
12x + y 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

16. Participant Scores 7 Cody Cremeans David Farrell Madison Dale
Hunter Wimmersberger
Katerah Ward

17. 1-4: The Distributive Property
Assignment
Page 29
1 – 47, odds