Warm ups
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Warm-ups. 3(x + 1) a(b + 2) x(y + z) 5(x + (-2) Use the distributive property to factor 2a + 2b ax + ay 3x + 3(-y). 3x + 3 ab +2a xy + xz 5x - 10 2(a + b) a(x + y) 3(x – y). Ch 2-7. Using the Distributive Property Algebra 1. Today’s Goals. Standards CA 1.0

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Warm-ups

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Warm ups

Warm-ups

  • 3(x + 1)

  • a(b + 2)

  • x(y + z)

  • 5(x + (-2)

    Use the distributive property to factor

  • 2a + 2b

  • ax + ay

  • 3x + 3(-y)

3x + 3

ab +2a

xy + xz

5x - 10

2(a + b)

a(x + y)

3(x – y)


Ch 2 7

Ch 2-7

Using the Distributive Property

Algebra 1


Today s goals

Today’s Goals

  • Standards

    • CA 1.0

      • Identify and use arithmetic properties

    • CA 2.0

      • Find Opposites

    • CA 4.0

      • Simplify Expressions

    • CA 10.0

      • Add and Subtract Monomials (like terms)


Ch 2 7 using the distributive property

Ch 2-7 Using the Distributive Property

The Distributive Property of Multiplication Over Addition

For any numbers a, b, c

a(b + c) = ab + ac

and

(b + c)a = ba + ca


Ch 2 7 using the distributive property1

Ch 2-7 Using the Distributive Property

The Distributive Property of Multiplication Over subtraction

For any numbers a, b, c

a(b – c) = ab – ac

and

(b – c)a = ba – ca


Ch 2 7 using the distributive property2

Ch 2-7 Using the Distributive Property

Example

7(8 – 3) = 7(8) – 7(3) = 35

7(8 – 3) = 7(5) = 35


Ch 2 7 using the distributive property3

Ch 2-7 Using the Distributive Property

Multiply.

  • 7(a – 2)

  • -5(u – v)

  • -6(2e – 3f – g)


Ch 2 7 using the distributive property4

Ch 2-7 Using the Distributive Property

Factoring is the reverse of the distributive property

Factor 5x – 5y

5(x – y)

Multiply 5(x – y)

5x – 5y


Ch 2 7 using the distributive property5

Ch 2-7 Using the Distributive Property

Factor

  • 3z -3y

  • 10u – 30

  • ua – ub – uc

  • 5x – 35y – 10

  • -6u – 4v – 8w

  • 14u – 21w – 28

3(z – y)

10(u – 3)

u(a – b – c)

5(x – 7y – 2)

-2(3u + 2v +4w)

7(2u – 3w – 4)


Ch 2 7 using the distributive property6

Ch 2-7 Using the Distributive Property

What are the terms of each expression?

  • 4a – 2b – 5c

    The terms are 4a, -2b, -5c

  • -8x + y – 7z

    The terms are -8x, y, -7z


Ch 2 7 using the distributive property7

Ch 2-7 Using the Distributive Property

What are the terms of each expression?

  • 4a – 2b – 5c

  • 18x + y – 7z

4a, -2b, -5c

18x, y, -7z


Ch 2 7 using the distributive property8

Ch 2-7 Using the Distributive Property

Collect like terms.

  • -7x + 2x – 3x

    (-7 + 2 – 3)x = -8x

  • 5x – 2y – 2x + 6y

    (5 - 2)x + (-2 + 6)x

  • 3.4a – 2.1a + 1.0a

    = 2.3a

  • -6a + 5b + 4a – b

    = -2a + 4b


Ch 2 8

Ch 2-8

Inverse of a Sum and Simplifying

Algebra 1


Ch 2 8 inverse of a sum and simplifying

Ch 2-8 Inverse of a Sum and Simplifying

The Property of -1

For any rational number a.

-1 · a = -a

(Negative one times a is the additive inverse of a.)


Ch 2 8 inverse of a sum and simplifying1

Ch 2-8 Inverse of a Sum and Simplifying

  • Is the additive inverse of 3 equal to additive inverse of -3?

    No

  • What is the additive inverse of 0?

    0

  • Write the additive inverse of x · y in 3 different ways

    -(x · y), (-x) · (y) and (x) · (-y)


Ch 2 8 inverse of a sum and simplifying2

Ch 2-8 Inverse of a Sum and Simplifying

Multiply

  • -1 · 12

  • -1 · (-4)

  • 0(-1)

    Rename each additive inverse without parentheses

  • -(2y + 3)

  • -(a – 2)

  • -(5y – 3z + 4w)

–12

4

0

– 2y – 3

– a + 2

–5y + 3z – 4w


Ch 2 8 inverse of a sum and simplifying3

Ch 2-8 Inverse of a Sum and Simplifying

a – (b + c) = a – b – c

Example

3 – (2 + 1)

3 – 2 – 1

= 0


Ch 2 8 inverse of a sum and simplifying4

Ch 2-8 Inverse of a Sum and Simplifying

Simplify:

  • 3 - (x + 1)

  • – (– 4a + 7b – 3c)

  • –(4ab – 5ac + 6bc)

  • 3 – (x + 1)

  • x – (2x – 3y)

  • 3z – 2y – (4z + 5y)

  • 7u – 3(7u + v)

  • -2(e – f) – (2e + 5f)

3 – x – 1 =2 - x

4a – 7b + 3c

– 4ab + 5ac – 6bc

2 – x

– x + 3y

– z – 7y

14u – 3v

4e – 3f


Ch 2 8 inverse of a sum and simplifying5

Ch 2-8 Inverse of a Sum and Simplifying

Simplify:

  • [5 + (3 + 1)]

    [5 + 4] = 9

  • {6 – [3 + (5 – 2)]}

    [6 – [3 + 3]} = {6 – 6} = 0

  • [3(2x – 1) + 1] – (3x + 1)

    [(6x – 3) + 1 = 3x – 1

    =6x – 3 + 1 – 3x – 1 = 3x - 3


Ch 2 9

Ch 2-9

Writing Equations

Algebra 1


By inserting grouping symbols how many different values can you give the expression 9 2 5 4 38

By inserting grouping symbols, how many different values can you give the expression9 • 2 + 5 • 4 = 38


Problem solving strategy

Problem Solving Strategy

Write an Equation


Warm ups

Ch 2-8 Inverse of a Sum and Simplifying

  • In two days Lupe hiked 65 km. She hiked 34.3 km the first day. How far did she hike the second day?

Let x = km that Lupe hiked the second day.

34.3 km

x

65 km

x = 65 - 34.3

65 = x + 34.3


Warm ups

Dan earns $3 for every lawn he mows. How many lawns must he mow to earn $54?

Let x = # of lawns mowed

$54 = x • $3


Warm ups

Tania sold three times as many tickets as Michele. Michele sold 16 tickets. How many did Tania sell?

Let T = tickets that Tania sold

T = 3 • 16

Michele = 16


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