1. Chapter 2 – Properties of Real Numbers
2.6 – The Distributive Property

2. 2.6 – The Distributive Property
Today we will learn how to:
Use the distributive property
Simplify expressions by combining like terms

3. 2.6 – The Distributive Property
Recall: Multiplying can be modeled as repeated addition.
5(2) =
5(2 + 4) =
5(2) + 5(4)
This is an example of the DISTRIBUTIVE PROPERTY

4. 2.6 – The Distributive Property
The product of a and (b + c):
a(b + c) = ab + ac
Example: 5(x + 2) = 5x + 5(2) = 5x + 10
(b +c )a = ba + ca
Example: (x + 4)8 = 8x + 8(4) = 8x + 32

5. 2.6 – The Distributive Property
The product of a and (b – c):
a(b – c) = ab – ac
Example: 4(x – 7) = 4x – 4(7) = 4x – 28
(b – c )a = ba – ca
Example: (x – 5)9 = 9x – (5)9 = 9x – 45

6. 2.6 – The Distributive Property
Example 1: Simplify
3(x + 1)
(x – 2)7
(2 + 5x)x
d(2 – d)

7. 2.6 – The Distributive Property
Example 2: Simplify
-6(x + 3)
(t + 2)(-3)
-1(1 – x)
(2x – 3)(-4x)

8. 2.6 – The Distributive Property
Example 3
Find the area of a rectangle whose width is 4 and whose length is x + 2.
x + 2 4

9. 2.6 – The Distributive Property
In a term that is the product of a number and a variable, the number is the COEFFICIENT of the variable.
Example: In the expression –x + 3y2, -1 and 3 are the coefficients

10. 2.6 – The Distributive Property
LIKE TERMS are terms in an expression that have the same variable raised to the same power.
Example: In the expression
–x2 + 5x + (-4) + (-3x) + 2,
5x and -3x are like terms;
-4 and 2 are like terms
-4 and 2 are also CONSTANT TERMS

11. 2.6 – The Distributive Property
The distributive property allows you to combine like terms that have variables by adding coefficients.
An expression is SIMPLIFIED if it has:
No grouping symbols
All of the like terms have been combined

12. 2.6 – The Distributive Property
Example 5
Simplify the expression
4x – x
5x2 – 7 + 3x2
1 – 4(1 – 2x)

13. 2.6 – The Distributive Property
Example 6
If takes you 30 minutes to get to school. You spend t minutes walking to the bus stop, and the rest of the time riding the bus. You walk 0.04 miles/minute and the bus travel 0.8 miles/minute. The total distance you travel is given by the function D = 0.04t + 0.8(30 – t). Simplify this function.

14. 2.6 – The Distributive Property
HOMEWORK
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