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Factoring the Sum and Difference of Two cubes

Factoring the Sum and Difference of Two cubes. a 3 + b 3 a 3 – b 3. Count. How long is the edge? How many squares in the face? How many blocks?. 1. 1. 1. Count. 2. 4. 8. Count. 2. 4. 8. 3. 9. 27. Count. n. n 2. n 3. 2. 4. 8. 3. 9. 27. 4. 16. 64. 5. 25. 125.

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Factoring the Sum and Difference of Two cubes

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  1. Factoring the Sum and Difference of Two cubes a3 + b3 a3 – b3

  2. Count • How long is the edge? • How many squares in the face? • How many blocks? 1 1 1

  3. Count 2 4 8

  4. Count 2 4 8 3 9 27

  5. Count n n2 n3 2 4 8 3 9 27 4 16 64 5 25 125

  6. Memorize the First 10 Perfect Cubes

  7. Recall the Difference of Two Squares Formula a2 – b2 =(a + b)(a – b) x2 – 9=(x + 3)(x – 3) • There are similar formulas for the sum and difference of two cubes.

  8. Multiply a Binomial by a Trinomial The Sum of Cubes

  9. Difference of Cubes

  10. Compare the Formulas The Sum of Cubes The Difference of Cubes They are just alike except for where they are different.

  11. Using the Difference of Cubes x3 - 8 Recall 23 = 8 = (x - 2)(x2 + 2x + 4)

  12. Using the Sum of Cubes y3 + 27 Recall 33 = 27 = (y + 3)(y2 – 3y + 9)

  13. Factor Out the Common Factor 3xa + 2x + 21a + 14 = 3xa + 2x + 3(7)a + 2(7)= x(3a + 2) + 7(3a + 2) = (3a + 2) ( x + 7 ) This is called factoring by grouping.

  14. What is factoring by grouping? Factoring a common monomial from pairs of terms, then looking for a common binomial factor is called factor by grouping. When do I use factoring by grouping? *when the problem consists of 4 terms How will my answer look? *it will be the product of two binomials

  15. Factor the expression Notice there are two terms Notice what each term has in common. Pull the common factor out of each term. Notice what is left in each term after factoring out the common factor.

  16. Try this example:

  17. Factor the polynomial Form two binomials with a + sign between them.

  18. Try this example:

  19. 6x2 – 3x – 4x + 2 by grouping 6x2 – 3x – 4x + 2 = (6x2 – 3x) + (– 4x + 2) = 3x(2x – 1) + -2(2x - 1) = (2x – 1)(3x – 2)

  20. Homework WB pp 89 and 90 Book p. 78 #1-27 0dd, p. 79 #1-27 odd

  21. Page 78

  22. Page 78

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