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Factoring Sum and Difference of two cubes.pptx

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This document outlines the objectives and methods for factoring the sum and difference of two cubes, including relevant formulas and detailed examples. It includes various exercises and quizzes to reinforce the material on factoring polynomials and recognizing differences of squares. Additional notes on perfect squares and complete factoring are also provided.

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Sum and Difference of Two Cubes
Objectives: In this lesson, you will be able to: Factor the sum and difference of two cubes completely and
EXPLORATION Complete the following products. 1. (x + 3) (x2 - 3x + 9) =x3 +____-3x2 -9x+_____+27 =x3 +___
EXPLORATION Complete the following products. 2. (x - 3) (x2 + 3x + 9) =___-3x2 +3x2 -___+9x-27 =___ - 27
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 x3 + y3 = (x+y) (x2 -xy+y2 ) x3 - y3 = (x-y) (x2 +xy+y2 )
Example 1: a. a3 +64 Factor each completely b. 8b3 + 27c3 = (a +4)(a2 - 4a+16) = (2b+3c)(4b2 - 6bc+9c2 ) Solution
QUIZ # 3: 1. 13 A. Evaluate: 2. 23 3. 33 4. 43 5. 53 6. 63 7. 73 8. 83 9. 93 10. 103
Quiz # 3 B. Factor each completely 11. m3 -64 12. 125+8q3 13. t3 -125s3 14. (u3 -8)(u3 +8) 15. 343v3 + 27w6
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.
Example 2: Factor each completely. a. 4a2 - 49 b. 9x2 - 25y4 c. 81 - 4p6 q4
Try it # 2: Factor each completely. a. 9a2 - 49 b. 64x2 - 25y4
If the terms of a binomial have a common factor, first factor out the common factor. Then continue factoring.
Example 3 Factor each completely a. 20x3 - 5x b. 112-175m4 c. 100x4 - 9x6
Try it # 3 Factor each completely a. 28x3 - 7x b. 128-200m4
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.
Example 4 Factor each completely a. 1 - 81x8 b. x4 y8 -z4
Try it # 4 Factor each completely a. 1 - 16x8 b. a4 -625b8
Quiz # 3 A. Tell whether or not the given polynomial is a difference of two squares. 1. a2 - 121 2. c2 - 18 3. d3 - 25 4. 25e2 - 16 5. 49f2 - 2g2 6. 64 +h2 7. 4m4 - 4n2 8. 2 (q2 - 4) 9. r2 - 9s4 10. t14 - u12
Quiz # 3 B. Factor each of the following completely 1. a4 - b6 2. c2 - 81 3. 4h2 - 49 4. 16j2 - 81k2 5. 1 - 25q4 6. 16r4 -121 7. 5t3 - 20t 8. 72v - 8v3 9. 144h2 - 49i2 10. (j+k)2 - 400

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Factoring Sum and Difference of two cubes.pptx

  • 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) (x2 - 3x + 9) =x3 +____-3x2 -9x+_____+27 =x3 +___
  • 4. EXPLORATION Complete the following products. 2. (x - 3) (x2 + 3x + 9) =___-3x2 +3x2 -___+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 x3 + y3 = (x+y) (x2 -xy+y2 ) x3 - y3 = (x-y) (x2 +xy+y2 )
  • 6. Example 1: a. a3 +64 Factor each completely b. 8b3 + 27c3 = (a +4)(a2 - 4a+16) = (2b+3c)(4b2 - 6bc+9c2 ) Solution
  • 7. QUIZ # 3: 1. 13 A. Evaluate: 2. 23 3. 33 4. 43 5. 53 6. 63 7. 73 8. 83 9. 93 10. 103
  • 8. Quiz # 3 B. Factor each completely 11. m3 -64 12. 125+8q3 13. t3 -125s3 14. (u3 -8)(u3 +8) 15. 343v3 + 27w6
  • 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. 4a2 - 49 b. 9x2 - 25y4 c. 81 - 4p6 q4
  • 11. Try it # 2: Factor each completely. a. 9a2 - 49 b. 64x2 - 25y4
  • 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. 20x3 - 5x b. 112-175m4 c. 100x4 - 9x6
  • 14. Try it # 3 Factor each completely a. 28x3 - 7x b. 128-200m4
  • 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 - 81x8 b. x4 y8 -z4
  • 17. Try it # 4 Factor each completely a. 1 - 16x8 b. a4 -625b8
  • 18. Quiz # 3 A. Tell whether or not the given polynomial is a difference of two squares. 1. a2 - 121 2. c2 - 18 3. d3 - 25 4. 25e2 - 16 5. 49f2 - 2g2 6. 64 +h2 7. 4m4 - 4n2 8. 2 (q2 - 4) 9. r2 - 9s4 10. t14 - u12
  • 19. Quiz # 3 B. Factor each of the following completely 1. a4 - b6 2. c2 - 81 3. 4h2 - 49 4. 16j2 - 81k2 5. 1 - 25q4 6. 16r4 -121 7. 5t3 - 20t 8. 72v - 8v3 9. 144h2 - 49i2 10. (j+k)2 - 400