Content Objective: Multiplying Polynomials

Linguistic Objective: to learn how to use vocabulary during activity and

homework

Do Now:

Simplify the Expression

(4x2 + 2x + 3) – (5x3 + 3x + 5)

3 2 1 0

Answers for Do Now

(4x2 + 2x + 3) – (5x3 + 3x + 5)

(4x2 + 2x + 3) + (-5x3 - 3x - 5)

3 2 1 0

+4x2 +2x+3

-5x3 -3x -5

-5x3 +4x2 -x -2

What are the pairs of like terms for each?

1. x, x2, -5x

2. a2, -4a2 , 2a, 5a4

3. 2xy2, -x2y, +xy2, -2x

4. c, -2, +4

5. x3, -2x4, 4x3, 3x2

6. +3rs, -rs2, +3r2, 3rs2

Vocabulary:

Monomial: An expression that consists of one term. Ex: Monolingual – one who speaks one language. Ex: 5xy

Binomial: An expression that consists of two terms. Ex: Bilingual – one who speaks two languages. Ex: 5x2 - 1

Vocabulary:(continued)

Trinomial: an expression that consists of three terms. Ex: Trilingual – on who speaks three languages. Ex: 5x3 + 3y2 - 6

Polynomial: An expression that contains one or more terms. A term is separated by plus or minus sign. Ex: 5x4 + 3xy5 – 3v7 + 3

Can you name these polynomials?

1. 5x – 6

2. -y

3. 3x2 + 5x + 7

4. 6ax7 + 9b4 + 9x3

5. 5

6. 1 + x

7. 2i + 3

8. 22

Multiplying Polynomials:Simplifying Expressions

2x2y2 • 4xRule: When multiplying polynomials, add the exponents of LIKE variables. * Multiply the coefficients

2 • 4 = 8x2 = x • x y2 = y • yx = x

The result is: 8x3y2

Multiplying Polynomials:Distributive Property

x2 (9x3 + 5x2y2)

Distributive Property: In this case distribute multiplication over addition. Ex: Think about the mailman that distributes mail throughout the community.

Multiplying Polynomials: Distributive Property

x2 (9x3 + 5x2y2)

Use Distributive Property to Multiply x2 into 9x3 and 5x2y2.

x2 • 9x3 + x2 • 5x2y2

Rule: Add the exponents of LIKE variables

Different View in Multiplying Polynomials

5x (9x3 – 5xy2 + 4)

We can demonstrate multiplication of polynomials a different way.

9x3 – 5xy2 + 4 5x

Different View in Multiplying Polynomials

9x3 – 5xy2 + 4 5x

Multiply 5x into each term.

Different Views in Multiplying Polynomials

9x3 – 5xy2 + 4 5x

5x times +4 5x times -5xy2 5x times 9x3.

9x3 – 5xy2 + 4 5x45x4 - 25x2y2 + 20x

Multiplying Polynomials

How did I get this result?

9x3 – 5xy2 + 4 5x45x4 - 25x2y2 + 20x

Guess Who Am I

In a rectangle I am the product of two sides.

Objective

To find the area and perimeter of figures using polynomials

Vocabulary

Perimeter: it is the measurement AROUND a figure. Ex: A fence around a house

Area: it is the measurement INSIDE a figure. Ex: The tiles on the floor of a classroom

Width: shorter side of a rectangle

Length: longer side of a rectangle

Properties of a Rectangle and Square

The rectangle has TWO pairs of equal sides.

ALL the sides of a square are equal.

The triangle has three sides.

Perimeter of a Rectangle

I want to put a fence around my yard. The lengthof my yard is 40 feet and the width is 10 feet.How many feet do I need to put a fence aroundmy yard?

*To find Perimeter

you add all sides*10 feet

40 feet

40 feet

10 feet

Perimeter of a Rectangle

I want to put a fence around my yard. The lengthof my yard is (4x + 5) feet and the width is(5) feet. How many feet do I need to put afence around my yard?

4x + 5

5 5

4x + 5

Area of a Rectangle

I want to put a rug on the floor of my room. Thelength of my room is 20 feet. The width of myroom is 6 feet. How much rug do I need for myroom?

*A of a = L • W 20 feet

6 feet

Area of a Rectangle

I want to put a rug on the floor of my room. Thelength of my room is (6x + 3) feet. Thewidth of my room is (5) feet. How much rug doI need for my room?

6x + 3

5

Activity:Find Area and Perimeter of each figure

1. 2. 3.

4. 5. 6.

2x + 3

3

3x2 + 4x

5

5x2 + 3x

2x

2xy + 3x

3x 5y2

3x2y5

Continued:Find Area and Perimeter of each Figure

7. 8. 9.

10. 11. 12.

5x

6x

5x2

4x

7x2 + 8x + 9

5x

6xy + 8x

3x5xy2z 3x2y

4 3x

Word Problems

The length of a rectangular poster is (5x + 4) inches and the width is 7x inches. The height of the chair is 22 inches. What is the area of the poster?

7x

5x + 4

Word Problem

Area of Rectangle = Length • Width

A = L • W

A of = (5x3z + 4y)(7xz)

Distributive Property

(7xz) (5x3z + 4y)

7xz • 5x3z 7xz • 4y

35 x4 z + 28 x y z

Multiplying Polynomials

5x3z + 4y

7xz

35x4z + 28xyz

Objective

Multiplying and Subtracting Polynomials using figures

Problem

Charlie had an expensive soccer ball that he had neverplayed with. His friends decided to invite himto play soccer. He decided to go, therefore, he brought hissoccer ball with him. The weather was amazing and theyplayed soccer for hours. They really had a great time.Suddenly, while Charlie went to the store to buy a drink,someone stole his soccer. When he came back to thesoccer field he realized his ball was missing. How can hefigure out who stole his soccer ball?

Thinking As A Detective

What is the area of the shaded portions of the figure?

8

12

10

Solving the Problem

1. Do you see any clues?

There are two rectangles. The bigger rectangle has a length of 12 and a width of 8. The smaller one has a length of 10 and a width of 8.

2. Break the problem into small parts.

First find the area of the bigger rectangle. Then find the area of the smaller rectangle. Then subtract the area of the smaller rectangle from the bigger one.

Sample Problem

What is the area of the shaded portions of the figure?

2x

3x3 + 5x + 2

4x - 3

Guide to Activity1. In pairs make your own two problems and switch your problems with two different groups. Use the steps used by a detective.

2. Do you see any clues?

3. What is your plan?

4. What is your solution? Show work!!!