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Polynomials Lesson 2Multiplying Binomials using Algebra tiles and Rectangle Diagrams
Todays Objectives
Students will be able to demonstrate an understanding of the multiplication of polynomial expressions, including: Multiply two polynomials symbolically, and combine
like terms in the product Generalize and explain a strategy for multiplication of
polynomials Express a polynomial as a product of its factors
Multiplying Binomials
Today we will look at two different strategies for multiplying binomials: Algebra Tiles Rectangle diagrams
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
x+3
x +
5
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
x+3
x +
5
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
Step 3: Draw the tiles
x+3
x +
5
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
Step 3: Draw the tiles
Step 4: Color the tiles
x+3
x +
5
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
Step 3: Draw the tiles
Step 4: Color the tiles
Step 5: Get the result
x+3
x +
5
(𝑥+3 ) (𝑥+5 )=𝑥2+5𝑥+3 𝑥+15=𝑥2+8 𝑥+15
Multiplying with Algebra Tiles (You do)
Step 1: Draw two dimensions, write polynomials beside them
x+2
2x-3
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
x+2
2x-3
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent polynomials
Step 3: Draw the tiles
x+2
2x-3
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent polynomials
Step 3: Draw the tiles
Step 4: Color the tiles
x+2
2x-3
Multiplying with Algebra Tiles
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent polynomials
Step 3: Draw the tiles
Step 4: Color the tiles
Step 5: Get the result
x+2
2x-3
(2 𝑥−3)(𝑥+2)=2𝑥 2+4 𝑥−3 𝑥−6=2𝑥 2+𝑥−6
If the numbers are big…
Rectangle Diagrams
x2 x2 -x
-x -x 1
-x -x 1
-x -x 1
2x2 -x
-6x 3
Multiplying with Rectangle Diagrams
12x + 32
23+
13x
Multiplying with Rectangle Diagrams
156x 2 416x
276x 736
12x + 32
23+
13x
Multiplying with Rectangle Diagrams
156x 2 416x
276x 736
12x + 32
23+
13x
(12 𝑥+32)(13 𝑥+23)=156𝑥 2+416 𝑥+276 𝑥+736=156 𝑥2+692𝑥+736
Ascending and Descending Order
Some questions will ask you to write your answer in ascending or descending order.
Ascending order: write each term in order of INCREASING exponent value:
Example)
Descending order: write each term in order of DECREASING exponent value:
Example)
ABCD Quiz
10 teams of 3, each with a scorekeeper
Each group member gets 4 pieces of paper A,B,C,D
For each question, teams will get 30 seconds to work out the answer
When I say “SLAP DOWN YOUR ANSWER!”, each team should SLAP your answers down on your desk
Team with the most correct answers get candy
People who volunteer to explain the answer get candy
1)
A)
B)
C)
D)
D
2)
A)
B)
C)
D)
A
3)
A)
B)
C)
D)
C
4)
A)
B)
C)
D)
B
5)
A)
B)
C)
D)
A
Homework
Pg. 166-167 #4-6,8,9,12,18,22
Pg. 177-178 #5-7,11