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The Distributive Property. The Distributive Property. The 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.

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## The Distributive Property

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**The Distributive**Property**The Distributive Property**The 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 Outsidethe parentheses with EVERYTHING INSIDE the parentheses.**Find the total area of the rectangles.Area = length x width**6 ft 6 ft 20 ft + 4 ft**One Way:**6(20) +6(4) Find the area of each rectangle. 6 ft 6 ft 120 sqft 24 sqft 20 ft + 4 ft**6(20) +6(4)**120 +24 = 144 sqft Now put the two rectangles back together. 6 ft 120 sq ft + 24 sq ft 24 ft**Second way:**Put the two rectangles together 6 ft 6 ft 20 ft + 4 ft**Second way:**6(20+4) 6(24) = 144 ft2 6 ft 144 sqft 20 ft + 4 ft**4**x 2 x +2 A Visual Example of the Distributive property Find the area of this rectangle. We could say that this is 4(x + 2) Or..**4**2 4 x So we can say that 4(x+2) = 4x+8**A swimming pool has a shallow end and a deep end. Find the**surface area of the pool. Deep water 8 yds shallow water 5 yds 10 yds**40 + 80 = 120 square yards**Or 8 ×15 = 120 square yards 40 80 8 yds 5 yds 10 yds**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**45+ 180 = 225 yds2**Or 9(25) = 225 yds2 (9 x 5) + (9 x 20) 0r 9(5+20) 9 yds (9 x 5) (9 x 20) 5 yds 20 yds

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