Download Lesson 15

Bell Quiz
Objectives
• Use the Distributive Property to simplify
expressions.
The Distributive Property
• The Distributive Property can be used to
simplify expressions.
The Distributive Property
For all real numbers a, b, c,
a(b + c) = ab + ac and a(b – c) = ab – ac
Examples
5(2 + 1) = 5 ∙ 2 + 5 ∙ 1 = 15
5(2 – 1) = 5 ∙ 2 – 5 ∙ 1 = 5
Example 1
Distributing a Positive Integer
Simplify each expression.
a. 6(4 + 8)
b. 4(5 – 3)
Lesson Practice
Simplify the expression.
8(2 + 7)
Lesson Practice
Simplify the expression.
4(6 – 2)
Example 2
Distributing a Negative Integer
Simplify each expression.
a. –(9 + 4)
b. – 9(– 6 – 3)
Lesson Practice
Simplify the expression.
–(9 + 3)
Lesson Practice
Simplify the expression.
– 14(4 – 2)
Example 3
Simplifying Algebraic Expressions
•
The Distributive Property applies not only to numeric
expressions but also to algebraic expressions.
Simplify each expression
a. – 4(x +7)
b. (5 – x)6
Lesson Practice
Simplify the expression.
– 10(m + 4)
Lesson Practice
Simplify the expression.
(7 – y)8
Example 4
Simplifying Algebraic Expressions with Exponents
Simplify each expression
a. mn(mx + ny + 2p)
b. – xy(y2 – x2z)
Lesson Practice
Simplify the expression.
4xy3(x4y – 5x)
Lesson Practice
Simplify the expression.
– 2x2m2 (m2 – 4m)
Example 5
Application
The turf on a football field is being
replaced. The field is 300 feet long and
160 feet wide, not including the two end
zones. Each end zone adds an additional
30 feet to the field’s length. Write an
expression using the Distributive
Property to show the entire area of the
field. Simplify the expression.
Lesson Practice
A group of 4 adults and 8 children are
buying tickets to an amusement park.
Tickets are $15 each. Write an expression
using the Distributive Property to show the
total cost of the tickets. Simplify the
expression.