1. Ch 10: Polynomials B) Multiplying Objective: To multiply polynomials using various techniques.

2. Methods for Multiplying Polynomials 1)Distributive Property 2)Long Multiplication 3)FOIL (First, Outside, Inside, Last) 4)Algebra Tiles

3. Distributive Property x (2x – 3) + 5(2x – 3) + (2x 2 – 3x)+(10x – 15)

4. (x + 3)(x + 4) Distributive Property Example 1 Example 2 x(x + 4) + 3(x + 4) + (x 2 + 4x)+(3x + 12) x 2 +7x + 12 (2a − 1)(a − 5) 2a(a − 5) − 1(a − 5) + (2a 2 -10a)+(−a + 5) 2a 2 -11a + 5

5. Long Multiplication (x+5)(2x – 3) * (x (2x (-3*5) (-3*x) (2x*5) (2x*x) + 5) - 3)

6. Polynomial Squares Common mistake! *

7. Long Multiplication ** Example 1 Example 2

8. FOIL (x+5) (2x – 3) F irst:  =2x 2 O utside:  =-3x I nside:  =10x L ast: 5 = -15 2x 2 + 7x - 15  x2x x-3 52x -3

9. FOIL Example 1 Example 2 y  y y  4 7  y 7  4 =y2y2 =4y =7y =28 x  x x  -8 3  x 3  =x2x2 =-8x = 3x =-24

10. Algebra Tiles (x+5) (2x – 3) x + 5 2x - 3 2 10 - 3= 7 - 15 Totals

11. Algebra Tiles Example 1 Example 2 m +2 m + 8 11016 x − 4 x − 5 1920

12. Classwork 1) 3) 2) 4)

13. 5) 7) 6) 8)