How do you expand linear expressions that involve

multiplication, addition, and subtraction?

For example, how do you expand 3(4 + 2x)?

In this lesson you will learn how to expand linear expressions with

rational coefficients by using the properties of real numbers.

Let’s ReviewLet’s Review

Vocabulary:Linear expression

Rational coefficientCombine like terms

2v + 3 + 7v - 1 = 9v

+ 2

Let’s ReviewLet’s Review

Properties of the Real Numbers:

Commutative: 11 + 4 = 4 + 11Associative: (4 + 3) + 9 = 4 + (3 +

9)Distributive: 5(6 + 2) = 5(6) + 5(2)

Let’s ReviewA Common Mistake

Failing to distribute negative numbers completely:

-9(4 + 3) = -9(4) + 9(3)-

Let’s ReviewA Common Mistake

=

Distributing multiplication over multiplication:

3(5 2) = 3(5) 3(2)-3(10)

15 6

30 90-

Let’s ReviewCore Lesson

Expand 3(2x + 4)

x x 1 1 1 1 2x + 4x x 1 1 1 1

x x 1 1 1 1

2x + 4

2x + 4

x 1

2x + 4

3

3(2x + 4) =

3(2x) + 3(4)

= 6x + 12

Let’s ReviewCore Lesson

11(3a - 2) - 6(8a - 9)

= 11(3a)

+ 11(-2)

+ (-6)(8a) + (-6)(-9)

= 11(3a - 2) + (-6)(8a - 9)

+ (-22) + (-48a)= 33a + 54

= -15a + 32

Expand and combine like terms:

In this lesson you have learned how to expand linear expressions with rational coefficients by using the

properties of real numbers.

Let’s ReviewGuided Practice

Simplify: 9(5k - 8) - 4(7 - 2k)

Let’s ReviewExtension Activities

Use a diagram to show why 4(3y + 2) = 12y + 8.

Let’s ReviewExtension Activities

Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y)

Let’s ReviewExtension Activities

Write at least two different linear expressions that expand and simplify to a value of 40x + 27.

Let’s ReviewQuick Quiz

1. Simplify: 7(3x-4) + 2(5 + 6x)

2. Simplify: 11(4 - 8w) - 6(-9w - 5)