Factoring Sum and Difference of two cubes.pptx

mathematics 8

1. Sum and Difference of Two Cubes

2. Objectives : In this lesson, you will be able to: Factor the sum and difference of two cubes completely and

3. EXPLORATION Complete the following products. 1. (x + 3) (x 2 - 3x + 9) =x 3 +____-3x 2 -9x+_____+27 =x 3 +___

4. EXPLORATION Complete the following products. 2. (x - 3) (x 2 + 3x + 9) =___-3x 2 +3x 2 -___+9x-27 =___ - 27

5. Extension: SUM AND DIFFERENCE OF TWO CUBES Let x and y be real numbers, variables, or algebraic expressions. Factoring Sum of Two Cubes Factoring Difference of Two Cubes x 3 + y 3 = (x+y) (x 2 -xy+y 2 ) x 3 - y 3 = (x-y) (x 2 +xy+y 2 )

6. Example 1: a. a 3 +64 Factor each completely b. 8b 3 + 27c 3 = (a +4)(a 2 - 4a+16) = (2b+3c)(4b 2 - 6bc+9c 2 ) Solution

7. QUIZ # 3 : 1. 1 3 A. Evaluate: 2. 2 3 3. 3 3 4. 4 3 5. 5 3 6. 6 3 7. 7 3 8. 8 3 9. 9 3 10. 10 3

8. Quiz # 3 B. Factor each completely 11. m 3 -64 12. 125+8q 3 13. t 3 -125s 3 14. (u 3 -8)(u 3 +8) 15. 343v 3 + 27w 6

9. Note: For a variable to be perfect square, it must be raised to an even power. The perfect integer squares less than 300 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, and 289.

10. Example 2: Factor each completely. a. 4a 2 - 49 b. 9x 2 - 25y 4 c. 81 - 4p 6 q 4

11. Try it # 2: Factor each completely. a. 9a 2 - 49 b. 64x 2 - 25y 4

12. If the terms of a binomial have a common factor, first factor out the common factor. Then continue factoring.

13. Example 3 Factor each completely a. 20x 3 - 5x b. 112-175m 4 c. 100x 4 - 9x 6

14. Try it # 3 Factor each completely a. 28x 3 - 7x b. 128-200m 4

15. After you have factored a difference of two squares, you can sometimes continue factoring. Factoring completely means to continue factoring until no further factors can be found.

16. Example 4 Factor each completely a. 1 - 81x 8 b. x 4 y 8 -z 4

17. Try it # 4 Factor each completely a. 1 - 16x 8 b. a 4 -625b 8

18. Quiz # 3 A. Tell whether or not the given polynomial is a difference of two squares. 1. a 2 - 121 2. c 2 - 18 3. d 3 - 25 4. 25e 2 - 16 5. 49f 2 - 2g 2 6. 64 +h 2 7. 4m 4 - 4n 2 8. 2 (q 2 - 4) 9. r 2 - 9s 4 10. t 14 - u 12

19. Quiz # 3 B. Factor each of the following completely 1. a 4 - b 6 2. c 2 - 81 3. 4h 2 - 49 4. 16j 2 - 81k 2 5. 1 - 25q 4 6. 16r 4 -121 7. 5t 3 - 20t 8. 72v - 8v 3 9. 144h 2 - 49i 2 10. (j+k) 2 - 400