Polynomials Lesson 2

1. 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

16. Multiplying with Rectangle Diagrams 12x + 32 23 + 13x

17. Multiplying with Rectangle Diagrams 12x + 32 23 + 13x

18. Multiplying with Rectangle Diagrams 12x + 32 23 + 13x (12x+32)(13x+23) = 156x2 + 416x + 276x + 736 = 156x2 + 692x + 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 x2 + 11x + 28 (x+7) (x+4) (x+6) (x-7) (x+47)(x+26) (2x+3) (3x-7) (31x-67) (49x+72) x2 – x - 42 x2 + 73x + 1222 6x2- 5x - 21 1519x2 - 1051x - 4824