1. 1/10/11 ©Evergreen Public Schools 2010 1 6/24/2010 ©Evergreen Public Schools 2010 1 Notes: 5 Methods to multiply binomials Double Distribution Stacking Box FOIL Smile Vocabulary: Distributive Property polynomial monomial binomial trinomial

2. 1/10/11 ©Evergreen Public Schools 2010 2 2 I can multiply polynomials and find common factors in polynomials. Give an example of a polynomial.

3. 1/10/11 ©Evergreen Public Schools 2010 3 3x(2x + 5) = 3x2x5+ 3x·· =6x 2 + 15x Remember the order of operations when simplifying… simplify multiplication before simplifying addition. Multiply coefficients, and watch the exponents!

4. 1/10/11 ©Evergreen Public Schools 2010 4  Be careful with negatives! -4x(3x - 7) = =-12x 2 + 28x -4x 3x - 7+ Look how “minus 7” changed to “plus negative 7”… Simplify… multiplication first! Multiply coefficients and watch the exponents… be careful of negatives! ( ) Circle all the polynomials you see on in the launch.

5. 1/10/11 ©Evergreen Public Schools 2010 5 5

6. 1/10/11 ©Evergreen Public Schools 2010 6 Factored form  (x + 2)(x + 3): › (x + 2) is one factor › (x + 3) is the other factor  A factor is anything you multiply › 3 times 4 is 12: › 3 and 4 are factors of 12.  A = l x w › length and width are factors Standard form  x 2 + 5x + 6 › It’s what you get after multiplying factors AND simplifying › It’s what you get after adding all the separate areas of your rectangle AND simplifying Factored Form vs Standard Form

7. 1/10/11 ©Evergreen Public Schools 2010 7 Factored Form = Length times Width: (x + 2) ( x + 3 ) (x + 2) Length times width always makes a rectangle. Finish your rectangle! Each rectangle is made up of lots of little rectangles. Use the dimensions to make your little rectangles. Your rectangle will have this length and width Once you have all your rectangles, count the areas to write the standard form. x2x2 xxx x x 1 1 1 1 1 1 Standard Form: +++++++++++ Standard Form (Simplified!): x 2 +5x +6 = x 2 + 5x + 6 (x + 3)(x + 2) Factored Form vs Standard Form Using Tiles

8. 1/10/11 ©Evergreen Public Schools 2010 8  area model  double distribution  stacking  FOIL  smile

9. 1/10/11 ©Evergreen Public Schools 2010 9  Think length times width: (2 x – 1)(4 x – 3) (2x – 1)(4x – 3) (2x (4x – 3) There are 4 distinct areas in the box. – 1 )

10. 1/10/11 ©Evergreen Public Schools 2010 10  Think length times width: (2x – 1)(4x – 3) (2x – 1)(4x – 3) (2x – 1) (4x – 3) Circle like terms. Simplify.

11. 1/10/11 ©Evergreen Public Schools 2010 11 is the distributive property, except the first factor is a binomial. (2x – 1) (4x – 3) =(2x – 1) +( ) = (2x – 1)·4x + (2x – 1)·(-3) Now distribute again. Twice! = 2x2x- 1 4x (-3) ( 4x)(-3)+ - 3 Notice the negative! (4x)+ (-1) = 8x 2 – 4x+ (-6x)+ 3Now combine like terms… = 8x 2 – 10x + 3

12. 1/10/11 ©Evergreen Public Schools 2010 12 ©Evergreen Public Schools 2010 12 Don’t forget tomorrow what you learned today!!! Write what you know about Factored Form Distributive Property Area Model Double Distribution

13. 1/10/11 ©Evergreen Public Schools 2010 13 ©Evergreen Public Schools 2010 13 Practice 7.6A Problem Numbers _______________

14. 1/10/11 ©Evergreen Public Schools 2010 14 ©Evergreen Public Schools 2010 14 5 3 1 2 4 Where are we now? I can multiply polynomials and find common factors in polynomials.

15. 1/10/11 ©Evergreen Public Schools 2010 15 ©Evergreen Public Schools 2010 15 Read your debrief from yesterday. Use Go Round 1 Protocol. Describe each word to your group. Factored Form Distributive Property Area Model Double Distribution

16. 1/10/11 ©Evergreen Public Schools 2010 16  Stacking works just like multiplying 34 and 97:  Now, instead of integers, we multiply our binomials 34 x 97 First multiply 7 & 4…. 8 Carry the 2 3 Then multiply 7 & 3 23 Then multiply 9 & 4 6 Carry the 3 Then multiply 9 & 3 31 Then ADD 3398 (2x - 1) ∙ (4x - 3) Multiply -3 & -1 +3 Multiply -3 and 2x -6x Multiply 4x & -1 -4x Multiply 4x & 2x 8x 2 Add like terms 8x 2 - 10x + 3 2

17. 1/10/11 ©Evergreen Public Schools 2010 17 First Outside Inside Last ( )( )– 14x4x – 32x2x 4x4x 2x2x 2 x (4 x ) – 32x2x 2 x (-3) – 14x4x -1(4 x ) – 1 – 3 -1(-3) = 8 x 2 = -6 x = -4 x = 3 8x28x2 - 6 x - 4 x + 3 8 x 2 – 10 x + 3 Combine like terms

18. 1/10/11 ©Evergreen Public Schools 2010 18 ( )( )– 14x4x – 32x2x 4x4x 2x2x 2 x (4 x ) – 32x2x 2 x (-3 x ) -1(4 x ) -1(-3) = 8 x 2 = -6 x = -4 x + 3.... What does this look like to you? 8x28x2 - 6 x - 4 x = 3 8 x 2 – 10 x + 3 Combine like terms

19. 1/10/11 ©Evergreen Public Schools 2010 19 ©Evergreen Public Schools 2010 19 Use 5 strategies. I will model Area Model Responsibility  double distribution  stacking  FOIL  smile

20. 1/10/11 ©Evergreen Public Schools 2010 20 ©Evergreen Public Schools 2010 20  Which method is your favorite? Why?  Tell you partner your favorite method and why its your favorite.

21. 1/10/11 ©Evergreen Public Schools 2010 21 ©Evergreen Public Schools 2010 21 5 3 1 2 4 Did you hit the target? I can multiply polynomials and find common factors in polynomials. Rate your understanding of the target from 1 to 5. 5 is a bullseye!

22. 1/10/11 ©Evergreen Public Schools 2010 22 ©Evergreen Public Schools 2010 22 Practice 7.6A Problem Numbers _______________