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Factoring Polynomials: Difference of Two Squares & Sum/Difference of Two Cubes

Learn how to factor polynomials using the difference of two squares and the sum/difference of two cubes methods. Examples included.

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Factoring Polynomials: Difference of Two Squares & Sum/Difference of Two Cubes

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  1. 6 Chapter Chapter 2 Factoring Polynomials

  2. Factoring Binomials Section 6.5

  3. Factoring the Difference of Two Squares Objective 1

  4. Difference of Two Squares A binomial is the difference of two squares if • both terms are squares and • the signs of the terms are different. For example, 9x2 – 25y2 –c4 + d4

  5. Difference of Two Squares • Factoring the Difference of Two Squares • a2 – b2 = (a + b)(a – b)

  6. Example Factor: x2 – 9. The first term is a square and the last term, 9, is a square and can be written as 32. The signs of each term are different, so we have the difference of two squares. x2 – 9 = (x – 3)(x + 3).

  7. Example Factor:

  8. Example Factor:

  9. Example Factor:

  10. Example Factor:

  11. Example Factor:

  12. Factoring the Sum or Difference of Two Cubes Objective 2

  13. Sum or Difference of Two Cubes a3 + b3 = (a + b)(a2 – ab + b2) a3 – b3 = (a – b)(a2 + ab + b2)

  14. Example • Factor x3 + 1. • Since this polynomial can be written as x3 + 13, • x3 + 1 = (x + 1)(x2 – x + 1).

  15. Example • Factor y3 – 64. • Since this polynomial can be written as y3 – 43, • y3 – 64 = (y – 4)(y2 + 4y + 16).

  16. Example • Factor 64y3 + 1. • 64y3 + 1 • = (4y + 1)(16y2 – 4y + 1)

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