Page 95 - Algebra 1

L E S S O N Using the Distributive Property to
15
Simplify Expressions
Warm Up
1. Vocabulary In the expression 3x + 5, 3x is a (variable, term) (2) of the expression.
Simplify each expression. 2. 5 - 7 + 5(3)
(4)
3. (-5) + (-2) + |(-5) + (-2)| (4)
4. Evaluate 7x + 4y for x = 2.1 and y = −0.7.
(9) _3 _4 _2
5. Find the product of 8, 5, and 3. (11)
New Concepts The Distributive Property can be used to simplify expressions. Since subtraction is the same as adding the opposite, the Distributive Property will
also work with subtraction.
Distributing a Positive Integer
Simplify each expression. a. 6(4 + 8)
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
Math Reasoning
Verify Use the order of operations to show that 4(5 - 3) = 8.
Online Connection www.SaxonMathResources.com
SOLUTION
6(4 + 8)
= 6(4) + 6(8) = 24 + 48
= 72
b. 4(5 - 3) SOLUTION
4(5 - 3)
= 4(5) + 4(-3) = 20 - 12
= 8
Distribute the 6. Multiply.
Add.
Distribute the 4. Multiply. Subtract.
80 Saxon Algebra 1