1. 1.7: Distributive Property
TERM: A number, a variable, or the product of the two. Ex: a, 3x, 2x, 5,
CONSTANT: a term with no variable (number) Ex: 4, -1, 6, 2

2. COEFFICIENT: Is the numerical factor of the a term. Ex: 3x, 5w, -3s,
LIKE TERMS: Term that have the same variable factors.
Ex: 7a and -3a, 4x and 12x, etc..

3. GOAL:

4. Distributive Property
Let a, b and c be real numbers.
ADDITION: a( b + c ) = ab + ac 3( x + 5 ) =
3x + 15
( b + c )a = ba + ca ( x + 5 )3 =
3x + 15
SUBTRACTION: a( b - c ) = ab - ac 3( x - 5 ) =
3x - 15
3x - 15
( b - c )a = ba - ca ( x - 5 )3 =

5. YOU TRY IT: What is the simplified form of: -2( 2y – 3x)?

6. - 2(2y – 3x) = = -4y + 6x SOLUTION:
Remember: if there is a negative sign, it always goes with the number at the right of it.
Using the distributive property we have:
- 2(2y – 3x) =
-2(2y) -2(-3x)
= -4y + 6x

7. REAL-WORLD:
The recommended hear rate for exercise, in beats per minute, is given by the expression 0.8(200 – y) where y is a person’s age in years. What is the recommended hear rate for a 14-year old student? Use the distributive property.

8. Substitute y for a 14 year old.
SOLUTION:
Using the given info and the distributive property we have:
Given: 0.8(200 – y)
Distribute: 0.8(200 – y) 
160 – 0.8y
Substitute y for a 14 year old.
160 – 0.8(14)
 160 – 11.2
 beats/min

9. Using Tiles and Models The area is an example of distributive property
Area = b ∙ h 2
Area = 2∙ (4 + 5) = 2(4) + 2(5) = 8+10 = 18 u2 4 5
Using Algebra we now have the following problem:
Area = b ∙ h 2
Area = 2 ∙ (4 + x)
= 2(4)+ 2(x)
= 2x + 8 u2 4 x

10. YOU TRY IT: What is the simplified form of: - ( -2y – 3x)?

11. - 1(-2y – 3x) = = 2y + 3x SOLUTION:
Remember: if there is only a negative sign next to the parenthesis, it is understood that there is a invisible 1 next to it:
Using the distributive property we have:
- 1(-2y – 3x) =
-1(-2y) -1(-3x)
= 2y + 3x

12. YOU TRY IT: What sum or difference is equivalent to 𝟕𝒙+𝟐 𝟓 ?

13. SOLUTION:
Using the opposite procedure we see that
𝟕𝒙+𝟐 𝟓
 𝟏 𝟓 𝟕𝒙+𝟐
 𝟕𝒙 𝟓 + 𝟐 𝟓

14. SIMPLY: Put (add or subtract) like terms together to make a smaller equation.
Ex:
Simplify: 2n + 1 – 4m – n + 2m
Solution: Re-write as:
= (2n- n)+(– 4m+2m) +1
= n– 2m+1

15. YOU TRY IT:
Rewrite each expression as a sum – 8x + 3xy – 2(3x) + 5xy

16. – 8x + 3xy – 6x + 5xy – 8x – 6x + 3xy + 5xy – 14x + 8xy SOLUTION:
Given: – 8x + 3xy – 2(3x) + 5xy
Doing the arithmetic (math) we have:
– 8x + 3xy – 6x + 5xy
Putting like terms together:
– 8x – 6x + 3xy + 5xy
– 14x + 8xy

17. Distributive Property
VIDEOS:
Distributive Property
Distribute:

18. Class Work:
Pages: 49 – 52
Problems: As many as you need to master the concepts.