Factoring the Sum or Difference of Two Cubes

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Factoring the Sum or Difference of Two Cubes

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  1. Factoring the Sum or Difference of Two Cubes

    Slide 1 - Factoring the Sum or Difference of Two Cubes

  2. Recognizing:

    Slide 2 - Recognizing:

    • a3 + b3 / a3 – b3
    • 8a3 + 27b3
    • (2a)3 + (3b)3
    • 128x3 – 54y3
    • 2(64x3 – 27y3)
    • 2[(4x)3 – (3y)3]
  3. Factoring:

    Slide 3 - Factoring:

    • Using the information given to us when we applied Division by Inspection, we get these general forms:
    • a3 + b3 = (a + b)(a2 – ab + b2)
    • a3 – b3 = (a – b)(a2 + ab + b2)
  4. Additional examples:

    Slide 5 - Additional examples:

    • Sometimes, you need to factor a number out of your exponent to get it to a cubed power.
    • r6 + s6
    • To get the powers of six (6) to cubed powers, simply divide them by 3
    • = (r2)3 + (s2)3
    • = (r2 + s2)[(r2)2 – r2s2 + (s2)2]
    • = (r2 + s2)(r4 – r2s2 + s4)
  5. Additional examples:

    Slide 6 - Additional examples:

    • Sometimes, you need to factor a number out of your exponent to get it to a cubed power.
    • a9 – 125b3
    • = (a3)3 – (5b)3
    • = (a3 – 5b)[(a3)2 + (a3)(5b) + (5b)2]
    • = (a3 – 5b)(a6 + 5a3b + 25b2)