THE DISTRIBUTIVE PROPERTY

The Distributive PropertyThe product of a and

(b+c):

a(b+c) = ab + ac

ex: 5(x + 2) = 5(x) + 5(2)

5x + 10

The product of a and (b-c):

a(b-c) = ab – ac

ex: 4(x –7)= 4(x) – 4(7)

4x –28

Sharing what is Outside the parentheses with EVERYTHING

INSIDE the parentheses.

Find the total area of the rectangles.Area = length x width

6 ft

20 ft + 4 ft

6 ft

One Way:6(20) +6(4)

6 ft

20 ft + 4 ft

6 ft

Find the area of each rectangle.

120 sq ft 24 sq ft

6(20) +6(4)120 +24 = 144 sq ft

6 ft

24 ft

Now put the two rectangles back together.

120 sq ft + 24 sq ft

Second way: Put the two rectangles together

6 ft

20 ft + 4 ft

6 ft

Second way:6(20+4)

6(24) = 144 ft2

6 ft

20 ft + 4 ft

144 sq ft

A Visual Example of the Distributive property

Find the area of this rectangle.

We could say that this is 4(x + 2)

x +2

Or..

x 2

4

x 2

44

)2(44 x 84 x

So we can say that

4(x+2) = 4x+8

Example using the distributive property

)5(2 x )(2 x )5(2

102 x

Another Example

)4(2 x )(2 x

82 x

)4(2

)4(3 x )(3 x

)12(3 x

Another Example

)4)(3(

123 xOr

)5(4 y )(4 y

)20(4 y

Another Example

)5)(4(

204 yOr

A swimming pool has a shallow end and a deep end. Find the surface area of the pool.

shallow waterDeep

water8 yds

5 yds 10 yds

80 408 yds

5 yds 10 yds

40 + 80 = 120 square yardsOr

8 ×15 = 120 square yards

You Try: Write two expressions that show how to find the total

area of the rectangle, then solve.(use the distributive property)

9 yds

5 yds 20 yds

(9 x 5) + (9 x 20) 0r

9(5+20)

9 yds

5 yds 20 yds

(9 x 5) (9 x 20)

45+ 180 = 225 yds2

Or

9(25) = 225 yds2