PreAlgebra

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Chapter 8 Expressions and Equations

8-4 Using the Distributive Property

Definition

The distributive property deals with combinations of multiplication and addition.

For any numbers a, b, and c:

a(b + c) = ab + ac

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Examples

Evaluate a(b+c) when a = 2, b = 3, and c = 4

Problem

Evaluate a(b+c)
when a = 2, b = 3, and c = 4

Substitute the given values

a(b+c) = 2(3 + 4)

Multiply (distributive property)

2(3 + 4)

= 2·3 + 2·4
= 6 + 8
= 14

Solution

a(b+c) = 14
when a = 2, b = 3, and c = 4

1. 3(5x + 4y) = 15x + 12y	2. 3(5w – 4z) = 15w – 12z
3. – 3(5u + 4v) = – 15u – 12v	4. – 3(5P – 4Q) = – 15P + 12Q

The distributive property allows any number of variables inside the parentheses. For example:

2(3x + 4y – 5z) = 6x + 8y – 10z

Examples

1. 3(5x + 4y + 2) = 15x + 12y + 6	2. 3(5w – 4z + k) = 15w – 12z + 3k
3. – 3(2t + 5u + 4v – 1) = – 6t –15u – 12v + 3	4. – 3(5P – 4Q + R – 0.5T) = – 15P + 12Q – 3R + 1.5T

Exercises

Click the ? symbol to see the correct answer.

Chapter 8 Expressions and Equations

8-3 Combining Like Terms

Like terms are expressions that have the same variable, or letter. Some examples of like terms are:

2x and 4x, y and 5y,

Examples

Combine like terms

1. 2x + 4x = 6x

2. 3x + 2x + 4 = 5x + 4

3. y + 3y + 2x = 4y + 2x

Exercises

Click the ? symbol to see the correct answer.

Author: David L. Heiserman
Publisher: SweetHaven Publishing Services