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