1. 8.5 – Factoring Differences of Squares

2. Recall:

3. Recall: Product of a Sum & a Difference

5. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b)

6. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2

7. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor!

8. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares!

9. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25

10. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n )(n )

11. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n + )(n – )

12. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n + 5)(n – 5)

13. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n + 5)(n – 5) b. 36x 2 – 49y 2

14. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n + 5)(n – 5) b. 36x 2 – 49y 2 ( x + )( x – )

15. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n + 5)(n – 5) b. 36x 2 – 49y 2 (6x + )(6x – )

16. Recall: Product of a Sum & a Difference (8.6) (a + b)(a – b) = a 2 – b 2 *Use in reverse to factor! *a and b MUST be perfect squares! Ex. 1 Factor each binomial below. a. n 2 – 25 (n + 5)(n – 5) b. 36x 2 – 49y 2 (6x + 7y)(6x – 7y)

17. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a

18. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a( )

19. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1)

20. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1)

21. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1)

22. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a( a + )( a – )

23. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a( a + )( a – )

24. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + )(2a – )

25. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + )(2a – )

26. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1)

27. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b. 2x 4 – 162

28. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2( )

29. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81)

30. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + )(x 2 – )

31. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9)

32. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9)

33. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9)

34. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9) 2(x 2 + 9)(x + )(x – )

35. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9) 2(x 2 + 9)(x + )(x – )

36. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9) 2(x 2 + 9)(x + 3)(x – 3)

37. Ex. 2 Factor each polynomial below. a. 48a 3 – 12a 12a(4a 2 – 1) 12a(2a + 1)(2a – 1) b.2x 4 – 162 2(x 4 – 81) 2(x 2 + 9)(x 2 – 9) 2(x 2 + 9)(x + 3)(x – 3)

38. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0

39. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + )(p – ) = 0

40. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0

41. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0

42. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1

43. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1

44. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x

45. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x

46. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0

47. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0

48. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x( x + )( x – ) = 0

49. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x(3x + )(3x – ) = 0

50. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x(3x + 5)(3x – 5) = 0

51. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x(3x + 5)(3x – 5) = 0 2x = 0

52. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x(3x + 5)(3x – 5) = 0 2x = 03x + 5 = 0

53. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x(3x + 5)(3x – 5) = 0 2x = 03x + 5 = 03x – 5 = 0

54. Ex. 3 Solve each equation by factoring. a. p 2 – 1 = 0 (p + 1)(p – 1) = 0 p + 1 = 0p – 1 = 0 - 1 - 1 + 1 + 1 p = -1 p = 1 b. 18x 3 = 50x - 50x -50x 18x 3 – 50x = 0 2x(9x 2 – 25) = 0 2x(3x + 5)(3x – 5) = 0 2x = 03x + 5 = 03x – 5 = 0 x = 0 x = -5/3 x = 5/3