Transcript Document

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
Let’s
Review
Vocabulary:
Linear expression
Rational coefficient
Combine like terms
2v + 3 + 7v - 1
= 9v + 2
Let’s
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Let’s
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Properties of the Real Numbers:
Commutative: 11 + 4 = 4 + 11
Associative: (4 + 3) + 9 = 4 + (3 + 9)
Distributive: 5(6 + 2) = 5(6) + 5(2)
A Common
Let’s
Review Mistake
Failing to distribute negative
numbers completely:
-9(4 + 3) = -9(4) + 9(3)
A Common
Let’s
Review Mistake
Distributing multiplication
over multiplication:
3(5 2) = 3(5) 3(2)
3(10)
30
=
15 6
90
CoreReview
Lesson
Let’s
Expand 3(2x + 4)
2x
3
3(2x + 4) =
x
x
x
+
x
x
x
3(2x)
4
1
1
1
1
1
1
1
1
2x + 4
2x + 4
1
1
1
1
2x + 4
+ 3(4)
= 6x + 12
CoreReview
Lesson
Let’s
Expand and combine like terms:
11(3a - 2) - 6(8a - 9)
= 11(3a - 2) + (-6)(8a - 9)
= 11(3a)+ 11(-2) + (-6)(8a) + (-6)(-9)
= 33a + (-22) + (-48a) + 54
= -15a + 32
In this lesson you have learned
how to expand linear expressions
with rational coefficients by using
the properties of real numbers.
Guided
Practice
Let’s
Review
Simplify: 9(5k - 8) - 4(7 - 2k)
Extension
Let’s
ReviewActivities
Use a diagram to show why
4(3y + 2) = 12y + 8.
Extension
Let’s
ReviewActivities
Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y)
Extension
Let’s
ReviewActivities
Write at least two different linear
expressions that expand and simplify
to a value of 40x + 27.
Quick Quiz
Let’s
Review
1. Simplify: 7(3x-4) + 2(5 + 6x)
2. Simplify: 11(4 - 8w) - 6(-9w - 5)