how do you expand linear expressions that involve multiplication, addition, and subtraction?

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)