1. Distributive Property
How to get rid of parentheses.

2. This basket contains 3 oranges, 2 red apples and 1 green apple.
Ah, Fruit
This basket contains 3 oranges, 2 red apples and 1 green apple.

3. How much fruit is there?
If I had 4 baskets, how much fruit would I have?
Duh, just dump them out on the table and count! OR

4. How much fruit is there?
They say that almost all things in nature can be modeled with math, so lets model it! 8 12

5. Lets model the 4 baskets with a 4 and a basket.
How much fruit is there?
We have 4 baskets of fruit where each basket contains 3 oranges, 2 red apples and 1 green apple
Lets model the 4 baskets with a 4 and a basket. 4

6. Lets model the basket as ( )4
and
and
We dropped the basket and used ( ) to represent the basket. Now we will use a + to represent the word “and” while we will replace each group with a single piece of fruit and the number for each of the fruits SO
Remember each basket contains 3 oranges, 2 red apples and 1 green apple.

7. Lets model the basket as4
and
and
This becomes … 4 3 2 1
Remember each basket contains 3 oranges, 2 red apples and 1 green apple.

8. Lets model the basket as4 3 2 1
Let’s now replace the orange with an X, the red apple with a Y and the green apple with a Z SO 4 3 X 2 Y 1 Z
Scary how all of a sudden delicious fruit becomes MATH

9. Lets model the basket as4 3 X 2 Y 1 Z
Remember that the 4 represented how many groups of 3 oranges we had and how many groups of 2 red apples and how many groups of green apples. SO
4 of
4 of 3 X
4 of 2 Y 1 Z
Scary how all of a sudden delicious fruit becomes MATH

10. Lets model the basket as
4 of
4 of 3 X
4 of 2 Y 1 Z
“of” is the math equivalent of multiply SO 4* 3 X 4* 2 Y 4* 1 Z
Scary how all of a sudden delicious fruit becomes MATH

11. Lets model the basket as4* 3 X 4* 2 Y 4* 1 Z
So what is 4*3 and 4*2 and 4*1? 12 X 8 Y 4 Z
Remember we started with fruit.

12. What just happened? 𝟒(𝟑𝒙+𝟐𝒚+𝒛) becomes 𝟒∙𝟑𝒙+𝟒∙𝟐𝒚+𝟒∙𝒛 or 𝟏𝟐𝒙+𝟖𝒚+𝟒𝒛
4 baskets of fruit became an equation. We noticed that we could get rid of the baskets or ( ) if we took each fruit or variable and multiplied by the number of baskets or 4. This process is called the distributive property – distributing the number multiplied outside the ( ) to each group inside and getting rid of the ( ).
𝟒(𝟑𝒙+𝟐𝒚+𝒛) becomes
𝟒∙𝟑𝒙+𝟒∙𝟐𝒚+𝟒∙𝒛 or
𝟏𝟐𝒙+𝟖𝒚+𝟒𝒛

13. Student Practice #1 Simplify using the distributive property
5(3𝑥+2𝑦+4𝑧)

14. Student Practice #1 solution
Simplify using the distributive property
5(3𝑥+2𝑦+4𝑧)
5∙3𝑥+5∙2𝑦+5∙4𝑧
Becomes
15𝑥+10𝑦+20𝑧

15. Student Practice #2 Simplify using the distributive property
4(5 𝑥 2 +2𝑥−7)

16. Student Practice #2 solution
Simplify using the distributive property
4(5 𝑥 2 +2𝑥−7)
4∙5 𝑥 2 +4∙2𝑥−4∙7
20 𝑥 2 +8𝑥−28
There are no like terms to combine

17. Student Practice #3 Simplify using the distributive property
−8(3 𝑥 2 +2𝑥𝑦−15 𝑦 2 )

18. Student Practice #3 solution
Simplify using the distributive property
−8(3 𝑥 2 +2𝑥𝑦−15 𝑦 2 )
−8∙3 𝑥 2 +−8∙2𝑥𝑦−−8∙15 𝑦 2
remember that a negative times a negative is a positive
−24 𝑥 2 −16𝑥𝑦+120 𝑦 2

19. Conclusion
In order to solve equations we often need to remove the ( ) so that we can combine or manipulate the terms. The distributive property gives us a way to remove the ( ).