1. Lesson 1.7 Distributive Property
Objective- To use the distributive property to simplify variable expressions.
Distributive Property
a(b + c) = ab + ac or
a(b - c) = ab - ac
Order of Operations
Distributive Property
6(3 + 5)
6(3 + 5)
6(8)
6(3) + 6(5) 48 48
Why distribute when order of operations is faster ?
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series
Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

2. Use the distributive property to simplify. 1) 3(x + 7) 6) x(a + m)
ax + am
2) 2(a - 4)
7) -4(-3 - r)
2a - 8
12 + 4r
3) -7(8 - m)
8) 2x(x - 8) m 2
2x - 16x
4) 3a(4 - a)
9) -5m(2m + 3) 2
12a - 3a 2
-10m - 15m
5) (3 - k)5
10) (6 - 2y)-3y
15 - 5k
6 - 5y
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3. 4(3 + 7) Geometric Model for Distributive Property 3 7 4 4
Two ways to find the total area.
Width by total length
Sum of smaller rectangles
4(3 + 7)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

4. = 4(3 + 7) 4(3) + 4(7) Geometric Model for Distributive Property 3 7 4 4
4(3)
4(7)
Two ways to find the total area.
Width by total length
Sum of smaller rectangles =
4(3 + 7)
4(3) + 4(7)
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

5. Subtracting a Quantity
1) -(x + 6)
6) -(3a + 1)
-x - 6
-3a - 1 2
2) -(2x - 8)
7) -(-3x + 2x -7) 2
-2x + 8
+3x - 2x + 7
3) 10- (4m + 3)
8) (3y - 8)
10 - 4m - 3
y + 8
- 4m + 7
- 3y - 4
4) 2(x - 5) - (x - 3)
9) 4(3k - 5) - (2k + 9)
2x x + 3
12k k - 9
x - 7
10k - 29
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

6. Simplify the following. 1) 10 - 4(x - 5) - 8 4) 5x - 4(7x - 9) - 11
Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series