1. Objective- To use the distributive property to simplify variable expressions.
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 ?

2. Use the distributive property to simplify.
1) 3(x + 7)
6) x(a + m)
3x + 21
ax + mx
2) 2(a - 4)
7) -4(3 - r)
2a - 8 r
3) -7(8 - m)
8) 2(x - 8) m
2x - 16
4) 3(4 - a)
9) -(2m - 3)
12 - 3a
-2m + 3
5) (3 - k)5
10) (6 - 2y)3
15 - 5k
18 - 6y

3. Use the distributive property to simplify. 1) 4(y - 7) 6) a(c + d)
ac + ad
2) 3(b + 4)
7) - (-3 - r)
3b + 12
3 + r
3) -5(9 - m)
8) 4x(x - 8) m 2
4x - 32x
4) 5a(4 - a)
9) -5m(2m + 3) 2
20a - 5a 2
-10m - 15m
5) (7 - k)6
10) (6 - 2y)-3y
42 - 6k
6 - 5y

4. 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)

5. = 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)

6. = 9(4 + x) 9(4) + 9(x) Geometric Model for Distributive Property 4 x 9
Two ways to find the total area.
Width by total length
Sum of smaller rectangles =
9(4 + x)
9(4) + 9(x)

7. Subtracting a Quantity
1) -(x + 6)
5) -(3a + 1)
-x - 6
-3a - 1 2
2) -(2x - 8)
6) -(-3x + 2x -7) 2
-2x + 8
+3x - 2x + 7
3) 10- (4m + 3)
7) (3y - 8)
10 - 4m - 3
y + 8
- 4m + 7
- 3y - 4
4) 2(x - 5) - (x - 3)
8) 4(3k - 5) - (2k + 9)
2x x + 3
12k k - 9
x - 7
10k - 29