1. Multiplying Binomials using Algebra tiles and Rectangle Diagrams
Polynomials Lesson 2
Multiplying Binomials using Algebra tiles and Rectangle Diagrams

2. 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

3. Multiplying Binomials
Today we will look at two different strategies for multiplying binomials:
Algebra Tiles
Rectangle diagrams

4. Multiplying with Algebra Tiles
x+3
Step 1: Draw two dimensions, write polynomials beside them
x + 5

5. Multiplying with Algebra Tiles
x+3
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
x + 5

6. Multiplying with Algebra Tiles
x+3
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
Step 3: Draw the tiles
x + 5

7. Multiplying with Algebra Tiles
x+3
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 + 5

8. Multiplying with Algebra Tiles
x+3
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 + 5
(x+3)(x+5) = x2 + 5x + 3x + 15 = x2 + 8x + 15

9. Multiplying with Algebra Tiles
x+2
Step 1: Draw two dimensions, write polynomials beside them
2x-3

10. Multiplying with Algebra Tiles
x+2
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent the two polynomials
2x-3

11. Multiplying with Algebra Tiles
x+2
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent polynomials
Step 3: Draw the tiles
2x-3

12. Multiplying with Algebra Tiles
x+2
Step 1: Draw two dimensions, write polynomials beside them
Step 2: Represent polynomials
Step 3: Draw the tiles
Step 4: Color the tiles
2x-3

13. Multiplying with Algebra Tiles
x+2
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
2x-3
(2x-3)(x+2) = 2x2 + 4x – 3x – 6 = 2x2 + x - 6

14. If the numbers are big…

15. Rectangle Diagrams x2 -x 1
2x2 -x
-6x 3

16. Multiplying with Rectangle Diagrams
12x x

17. Multiplying with Rectangle Diagrams
12x
156x 2
416x
276x
736 x

18. Multiplying with Rectangle Diagrams
12x
156x 2
416x
276x
736 x
(12x+32)(13x+23) = 156x x + 276x = 156x x + 736

19. 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: 5 – 3x + 2x2 + 4x3
Descending order: write each term in order of DECREASING exponent value.
Example: 4x3 + 2x2 – 3x + 5

20. Review Quiz
(x+7) (x+4) (x+6) (x-7) (x+47)(x+26) (2x+3) (3x-7) (31x-67) (49x+72)
x2 + 11x + 28
x2 – x - 42
x2 + 73x
6x2 - 5x - 21
1519x x