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# Integrated Math 2 Section 9-8

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Perfect Squares and Differences of Squares

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### Integrated Math 2 Section 9-8

1. 1. SECTION 9-8 Perfect Squares and Diﬀerences of Squares
2. 2. Essential Questions How do you factor perfect square trinomials? How do you factor the diﬀerence of perfect squares? Where you’ll see this: Travel, number sense, modeling, geography
3. 3. Vocabulary 1. Perfect Square Trinomial: 2. Diﬀerence of Two Squares:
4. 4. Vocabulary 1. Perfect Square Trinomial: A trinomial that can be factored into a binomial squared 2. Diﬀerence of Two Squares:
5. 5. Vocabulary 1. Perfect Square Trinomial: A trinomial that can be factored into a binomial squared 2. Diﬀerence of Two Squares: A polynomial that can be factored into two binomials with the same terms but diﬀerent signs in between
6. 6. Perfect Square Trinomial 2 ( a − b)
7. 7. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b)
8. 8. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b
9. 9. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
10. 10. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
11. 11. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
12. 12. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b
13. 13. Perfect Square Trinomial 2 ( a − b) ( a − b)( a − b) 2 2 a − ab − ab + b 2 2 a − 2ab + b First term squared, last term squared, middle term is 2 times ﬁrst term times last term
14. 14. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 c. x − 14x + 49 d. x + 7x + 14
15. 15. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 (3x 2 2 c. x − 14x + 49 d. x + 7x + 14
16. 16. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 (3x +2) 2 2 c. x − 14x + 49 d. x + 7x + 14
17. 17. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 (3x +2) (y 2 2 c. x − 14x + 49 d. x + 7x + 14
18. 18. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 (3x +2) ( y −10) 2 2 c. x − 14x + 49 d. x + 7x + 14
19. 19. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 (3x +2) ( y −10) 2 2 c. x − 14x + 49 d. x + 7x + 14 2 ( x − 7)
20. 20. Example 1 Factor. 2 2 a. 9x + 12x + 4 b. y − 20 y + 100 2 2 (3x +2) ( y −10) 2 2 c. x − 14x + 49 d. x + 7x + 14 2 ( x − 7) Not a perfect square trinomial
21. 21. Difference of Squares ( a − b)( a + b)
22. 22. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b
23. 23. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b
24. 24. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b
25. 25. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b
26. 26. Difference of Squares ( a − b)( a + b) 2 2 a + ab − ab − b 2 2 a −b First term squared, last term squared, subtraction between the two terms
27. 27. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
28. 28. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
29. 29. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
30. 30. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
31. 31. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
32. 32. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 4 4 8 2 e. 25x y − 36z f. 16h − 144
33. 33. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) 4 4 8 2 e. 25x y − 36z f. 16h − 144
34. 34. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) 4 4 8 2 e. 25x y − 36z f. 16h − 144
35. 35. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a diﬀerence of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144
36. 36. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a diﬀerence of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 (5x y + 6z )
37. 37. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a diﬀerence of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 2 2 4 (5x y + 6z ) (5x y − 6z )
38. 38. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a diﬀerence of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 2 2 4 (5x y + 6z ) (5x y − 6z ) (4h + 12)
39. 39. Example 2 Factor. 2 2 a. 64x − 81 b. r − 121 (8x −9) (8x + 9) (r + 11) (r − 11) 2 2 c. t − 900 d. y + 100 (t + 30) (t − 30) Not a diﬀerence of squares 4 4 8 2 e. 25x y − 36z f. 16h − 144 2 2 4 2 2 4 (5x y + 6z ) (5x y − 6z ) (4h + 12) (4h − 12)
40. 40. Homework
41. 41. Homework p. 410 #1-42 multiples of 3 “There are two kinds of men who never amount to much: those who cannot do what they are told and those who can do nothing else.” - Cyrus H. Curtis