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Content Objective: Multiplying Polynomials
Linguistic Objective: to learn how to use vocabulary during activity and
homework
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 Views in Multiplying Polynomials
9x3 – 5xy2 + 4 5x
5x times +4 5x times -5xy2 5x times 9x3.
9x3 – 5xy2 + 4 5x45x4 - 25x2y2 + 20x
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
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?
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.
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