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 Review Vocabulary: Linear expression Rational coefficient Combine like terms 2v v - 1 = 9v + 2

Let’s Review Properties of the Real Numbers: Commutative: = Associative: (4 + 3) + 9 = 4 + (3 + 9) Distributive: 5(6 + 2) = 5(6) + 5(2)

A Common Mistake Failing to distribute negative numbers completely: -9(4 + 3) = -9(4) + 9(3) -

Let’s Review A Common Mistake = Distributing multiplication over multiplication: 3(5 2) = 3(5) 3(2) - 3(10)

Let’s Review Core Lesson Expand 3(2x + 4) xx x + 4 xx 1111 xx 1111 x 1 2x (2x + 4) = 3(2x) + 3(4)= 6x + 12

Let’s Review Core 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 Review Guided Practice Simplify: 9(5k - 8) - 4(7 - 2k)

Let’s Review Extension Activities Use a diagram to show why 4(3y + 2) = 12y + 8.

Let’s Review Extension Activities Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y)

Let’s Review Extension Activities Write at least two different linear expressions that expand and simplify to a value of 40x + 27.

Let’s Review Quick Quiz 1. Simplify: 7(3x-4) + 2(5 + 6x) 2. Simplify: 11(4 - 8w) - 6(-9w - 5)