1-5 The Distributive Property
pages 25-31
Vocabulary:
Term-a number, a variable, or a product or quotient of
numbers and variables.
Like Terms-terms that contain the same variables, with
corresponding variables having the same exponent.
Equivalent Expressions-expressions that denote the same
number.
Simplest Form-an expression is in simplest form when it is
replaced by an equivalent expression having no like terms or
parentheses.
Coefficient-the numerical factor of a term.
Your Turn!
Ex.15 Using the distributive property, solve each equation.
a. 2(2 + x)
4 + 2x
b. y(a - 3)
ay -3y
c. x(1 + y)
x + xy
Distributive Property
"Distribute one number to the rest"
Ex.1 x(8+3) = 8x + 3x
For any numbers a, b, and c:
a(b+c) = ab + ac and (b+c)a = ba + ca
a(b-c) = ab – ac
and (b-c)a = ba – ca
Ex.2 2(4+t) = 8 + 2t
Ex.3 8(3m + 6) = 24m + 48
Example 1: Distribute Over Addition
Rewrite 8(10 + 4) using the Distributive Property. Then evaluate.
8(10 + 4) =8(10) + 8(4)
=80 + 32
=112
Distributive Property
Multiply.
Add.
Example 3: Use the Distributive Property
Example 2: Distribute Over Subtraction
Rewrite (12-3)6 using the Distributive Property. Then evaluate.
(12-3)6=12 6-3 6
=72-18
=54
Distributive Property
Multiply.
Add.
CARS The Morris family owns two cars. In 1998, they drove
the first car 18,000 miles and the second car 16,000 miles.
Use the graph to find the total cost of operating both cars.
Use the Distributive Property to write and evaluate an
expression.
0.46(18,000 + 16,000)
=8280 + 7360
=15,640
DistributiveProp.
Multiply.
Add.
It cost the Morris family $15,640 to operate their cars.
Example 4: Use the Distributive Property
Example 5: Algebraic Expressions
Use the Distributive Property to find each product.
a. 15 99
15 99=15(100-1)
Think: 99=100-1
Distributive Property
=15(100-15(1)
Multiply.
=1500-15
Subtract.
=1485
Rewrite each product using the Distributive Property. Then
simplify.
a. 5(g-9)
2
1
b. 35(2 5 )
1
1
35 ( 2 5 )=35 ( 2 + 5 )
1
=35 (2) + 35 (5 )
=70 + 7
=77
b. 3(2x + 4x-1)
1
1
Think: 2 = 2 +
5 Property
5
Distributive
Multiply.
Add.
Example 6: Combine Like Terms
Simplify each expression
33x
a. 15x + 18x
2
2
b. 10n + 3n + 9n
2
10n + 12n