The Distributive PropertySection 2.7

Find the area

You are planting a vegetable garden and a flower garden. The diagram shows the dimensions of the two adjacent gardens.

How can you find the total area of the two gardens? (Show more than one method)

16 ft

8 ft

12 ft

8 ft

1. Find the area of each garden and then add the areas together.

Area = 8(12) + 8(16)Area = 96 + 128Area = 224 square feet

2. Find the total length then multiply it times the common width

Area = 8 ( 12 + 16)Area = 8 (28)Area = 224 square feet

Distributive Propertya(b+c) = ab + ac 9(2+6) = 9(2) + 9(6)a(b-c) = ab – ac 8(7-1) = 8(7) –

8(1)

Example 1 Use the distributive property

-4(a + 13) =

5(2 – x + 3y) =

Example 2: Simplify the expressions(distribute and combine like terms)

2(9+ y) + 3 y -7 ( 3x-1) + y - 2

Your turn: Use the distributive property to simplify and combine like terms

1. -3(8+ w)= 2. 6(2y – 15)=

Your turn: Use the distributive property to simplify and combine like terms

4. 6( t – 7 ) – t + 12

5. 6 – 4(2w – 5) Be careful on this one!

6. Write two expressions for the total area of the two rectangles

10 ft 10 ft

12 ft 22 ft

7. Write two expressions for the total area of the two rectangles

5 ft 5 ft

x ft 14 ft