1. Algebra 3 Lesson 2.1 Objective: SSBAT multiply polynomial expressions. Standards: M11.D.2.2.1

2. Algebra 3 Warm-Up 2.1 Multiply each. 1.9x 2 ∙ 3x 4 ∙ 2x 3 2.10mn ∙ -12mn 3. -7x 5 y 2 ∙ -2xy 6

3. Examples: Multiply each. 1.3x(x 3 – 7x 2 + 8x – 2) = 3x 4 – 21x 3 + 24x 2 – 6x 2.x 3 (5x 2 – 12x + 8) = 5x 5 – 12x 4 + 8x 3

4. 3. (x + 2)(x – 3) = x 2 – 3x + 2x – 6 = x 2 – 1x – 6  FOIL

5. 4. (2x + 9)(3x – 5) = 6x 2 – 10x + 27x – 45 = 6x 2 + 17x – 45

6. 5. (5x – 7)(5x + 7) = 25x 2 + 35x – 35x – 49 = 25x 2 – 49

7. 6.(3x 2 – 5)(4x 2 – 2)

8. 7.(m 2 – 5n 2 )(2m 2 + 3n 2 )

9. 8.5(x – 1)(2x + 3)  Work with 2 at a time 5(x – 1) = 5x – 5 Then: (5x – 5)(2x + 3) = 10x 2 + 15x – 10x – 15 = 10x 2 + 5x – 15

10. 9.3x(x – 5)(x – 4) 3x(x – 5) = 3x 2 – 15x Then: (3x 2 – 15x)(x – 4) = 3x 3 – 12x 2 – 15x 2 + 60x = 3x 3 – 27x 2 + 60x

11. 10.(x + 2)(x 2 – 5x + 8) = x 3 – 5x 2 + 8x + 2x 2 – 10x + 16 = x 3 – 3x 2 – 2x + 16

12. 11. (x – 3)(2x 2 + x – 9) = 2x 3 + x 2 – 9x – 6x 2 – 3x + 27 = 2x 3 – 5x 2 – 12x + 27

13. 12. (x – 4) 2 = (x – 4)(x – 4) = x 2 – 4x – 4x + 16 = x 2 – 8x + 16

14. 13. Find the Area of a Rectangle whose width is (x + 7) units and length is (x 2 – 2x + 11) units.  A = lw A = (x + 7)(x 2 – 2x + 11) A = x 3 – 2x 2 + 11x + 7x 2 – 14x + 77 A = x 3 + 5x 2 – 3x + 77 units 2

15. 14.Which has a greater Area, a square with a side that is (x + 3) units long or a Rectangle with a width of x units and a length of (x + 6) units? Area of Rectangle: A = lw Find Area of Square  A = (x + 3)(x + 3) = x 2 + 3x + 3x + 9 = x 2 + 6x + 9 Find Area of Rectangle  A = x(x + 6) = x 2 + 6x The Area of the Square is Greater.

16. Quadratic Equation  An equation of the form, ax 2 + bx + c = 0  There is an exponent of 2 and that is the highest exponent  Examples: 5x 2 – 3x + 8 = 0 9x 2 – 7 = 0 -5x 2 = 0

17. Determine if each of the following is a Quadratic Equation or not. (you may need to simplify first) 1.5x 3 – 6x 2 – 3x + 18 = 0  No 2. 8 – 7x + 12x 2 = 0  Yes

18. 3. (x – 2)(x + 8) = 0 x 2 + 8x – 2x – 16 = 0 x 2 + 6x – 16 = 0  Yes

19. 4. -15x 2 – 12 = 0  Yes 5.7x – (15x + 6x 2 ) + 6x 2 = 0 7x – 15x – 6x 2 + 6x 2 = 0 -8x = 0  No

20. On Your Own. Multiply each. 1.(x – 7)(x – 9) 2.x(x + 5)(3x + 7)

21. Homework Worksheet 2.1