The Distributive Property
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![Page 1: The Distributive Property](https://reader036.fdocuments.in/reader036/viewer/2022083004/56812c9d550346895d91442e/html5/thumbnails/1.jpg)
THE DISTRIBUTIVE PROPERTY
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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.
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Find the total area of the rectangles.Area = length x width
6 ft
20 ft + 4 ft
6 ft
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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
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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
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Second way: Put the two rectangles together
6 ft
20 ft + 4 ft
6 ft
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Second way:6(20+4)
6(24) = 144 ft2
6 ft
20 ft + 4 ft
144 sq ft
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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
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x 2
44
)2(44 x 84 x
So we can say that
4(x+2) = 4x+8
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Example using the distributive property
)5(2 x )(2 x )5(2
102 x
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Another Example
)4(2 x )(2 x
82 x
)4(2
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)4(3 x )(3 x
)12(3 x
Another Example
)4)(3(
123 xOr
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)5(4 y )(4 y
)20(4 y
Another Example
)5)(4(
204 yOr
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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
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80 408 yds
5 yds 10 yds
40 + 80 = 120 square yardsOr
8 ×15 = 120 square yards
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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
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(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