Objectives• Multiply expressions containing

variables. • Divide expressions containing

variables.

Page 96 Multiplying and Dividing Expressions

Why?When solving equations, you often need to multiply or divide not only single numbers, but also larger expressions that may include variables.

Glossary Terms2.7 Multiplying and Dividing Expressions

4² = 16base

exponent

power

x²

Multiply ExpressionsMultiply the following expressions

2x(3x – 4)Use the distributive property2x(3x) – 2x(4)

Multiply6x² - 8x

(-2)(5a – 4)Use the distributive property-2(5a) – (-2)(4)Multiply-10a – (-8) Simplify using the definition of subtraction-10a + 8

Multiply ExpressionsSimplify the following

(5x + 3y – 7) – 3(2x – y)Use the definition of subtraction to rewrite the expression as an addition problem.

(5x + 3y – 7) + (-3)(2x – y)

Use the distributive property5x + 3y – 7 – 6x + 3y

Combine like terms(5x – 6x) +(3y + 3y) - 7

-x + 6y - 7

Divide ExpressionsTo divide expressions, rewrite using the rules for fractions. Then use what you know about canceling to simplify.

Dividing an expression:a + b c = a

c + bc

2 + 3 7 = 2

7 + 37

2x + 6 2 = 2x

2 + 62

Simplify the following2x² + 6 2

Split up the fraction2x² 2 + 6

2

Simplify each fractionx² + 3

Key SkillsMultiply and divide expressions.

b. (5x + 9) – 2(x + 3)

(5x + 9) –2(x) + (–2)(3)

5x + 9 – 2x – 6

Distributive Property

Group like terms.

3x + 3 Simplify.

Key SkillsMultiply and divide expressions.

4k2 + k + 9

Rule for Dividing an Expression

Simplify.

c. 12k2 + 3k + 27

312k2

33k3

273

+ +

TOC

AssignmentPage 101 -103

# 18 – 48 even, 62 – 86 even