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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. Vocabulary: - PowerPoint PPT Presentation
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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)