how do you expand linear expressions that involve multiplication, addition, and subtraction?
DESCRIPTION
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 PresentationTRANSCRIPT
![Page 1: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/1.jpg)
How do you expand linear expressions that involve
multiplication, addition, and subtraction?
For example, how do you expand 3(4 + 2x)?
![Page 2: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/2.jpg)
In this lesson you will learn how to expand linear expressions with
rational coefficients by using the properties of real numbers.
![Page 3: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/3.jpg)
Let’s ReviewLet’s Review
Vocabulary:Linear expression
Rational coefficientCombine like terms
2v + 3 + 7v - 1 = 9v
+ 2
![Page 4: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/4.jpg)
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)
![Page 5: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/5.jpg)
Let’s ReviewA Common Mistake
Failing to distribute negative numbers completely:
-9(4 + 3) = -9(4) + 9(3)-
![Page 6: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/6.jpg)
Let’s ReviewA Common Mistake
=
Distributing multiplication over multiplication:
3(5 2) = 3(5) 3(2)-3(10)
15 6
30 90-
![Page 7: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/7.jpg)
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
![Page 8: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/8.jpg)
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:
![Page 9: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/9.jpg)
In this lesson you have learned how to expand linear expressions with rational coefficients by using the
properties of real numbers.
![Page 10: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/10.jpg)
Let’s ReviewGuided Practice
Simplify: 9(5k - 8) - 4(7 - 2k)
![Page 11: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/11.jpg)
Let’s ReviewExtension Activities
Use a diagram to show why 4(3y + 2) = 12y + 8.
![Page 12: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/12.jpg)
Let’s ReviewExtension Activities
Simplify: 5(7y + 1) - 2(9y - 10) + 3(18 - 4y)
![Page 13: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/13.jpg)
Let’s ReviewExtension Activities
Write at least two different linear expressions that expand and simplify to a value of 40x + 27.
![Page 14: How do you expand linear expressions that involve multiplication, addition, and subtraction?](https://reader034.vdocuments.us/reader034/viewer/2022051518/56815b5a550346895dc940c8/html5/thumbnails/14.jpg)
Let’s ReviewQuick Quiz
1. Simplify: 7(3x-4) + 2(5 + 6x)
2. Simplify: 11(4 - 8w) - 6(-9w - 5)