Lab: Distributive Property Name: ______
A flower bed is being made in the picnic area. The flower bed will contain two types of flowers.
1. What is the area of the flower bed? ______How did you determine your answer?
The flower bed problem illustrates the distributive property. This lab will examine the distributive property. Problems such as the one above can be modeled with Algebra Lab Gear as shown below.
The lab gear can also be used to illustrate the distributive property using variables.
Example 1: 2(x + 5)
I. Using the algebra lab gear, simplify each of the following expressions. Draw your solution on the corner piece.
1. 5 (x + 5) = ______2. 3 (x + 4) = ______
3. 3 (2x + 1) = ______4. 5 (x + y) = ______
5. x (x + 3) = ______6. x (2x + 4) = ______
7. y (x + 2) = ______8. (x + 3)(x + 5) =______
9. (x + 3)2 = ______10. (x + 1) (x + 2) = ______
II. Simplify the following. Make a sketch of the algebra lab gear to help you if needed.
11. 6 (x + 3) = ______
12. 4 (x + 7) = ______
13. 5 ( 2x + 5) = ______
14. 2 (3x + 3) = ______
15. x (x + 5) = ______
16. 2x (y + 2) = ______
III. Find the areas of the squares and rectangles with the following dimensions:
17. (x + 3)(x + 2) = ______
18. (x + 4)2 = ______
19. (x + 5)(x + 1) = ______
20. y(x + 7) = ______
Answer Key
I. Using the algebra lab gear, simplify each of the following expressions. Draw your solution on the corner piece.
1. 5 (x + 5) = 5x + 25 2. 3 (x + 4) = 3x + 12
3. 3 (2x + 1) = 6x + 3 4. 5 (x + y) = 5x + 5y
5. x (x + 3) = x2 + 3x 6. x (2x + 4) = 2x2 + 4x
7. y (x + 2) = xy + 2y 8. (x + 3)(x + 5) = x2 + 8x + 15
9. (x + 3)2 = x2 + 6x + 9 10. (x + 1) (x + 2) = x2 + 3x + 2
II. Simplify the following. Make a sketch of the algebra lab gear to help you if needed.
11. 6 (x + 3) = 6x + 18
12. 4 (x + 7) = 4x + 28
13. 5 (2x + 5) = 10x + 25
14. 2 (3x + 3) = 6x + 6
15. x (x + 5) = x2 + 5x
16. 2x (y + 2) = 2xy + 4x
III. Find the areas of the squares and rectangles with the following dimensions:
17. (x + 3)(x + 2) = x2 + 5x + 6
18. (x + 4)2 = x2 + 8x + 16
19. (x + 5)(x + 1) = x2 + 6x + 5
20. y(x + 7) = xy + 7y