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Section 5.5. Special Factoring Formulas. The Difference of Two Squares. a 2 – b 2 = (a + b)(a – b) Examples: 1) 64x 2 – 9 2) 49x 2 – 81y 2 3) 169x 4 – 9y 4 4) x 6 – y 8. The Sum and Difference of Two Cubes. a 3 + b 3 = (a + b)(a 2 – ab + b 2 )

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section 5 5

Section 5.5

Special Factoring Formulas

the difference of two squares
The Difference of Two Squares
  • a2 – b2 = (a + b)(a – b)
  • Examples:
  • 1) 64x2 – 9 2) 49x2 – 81y2
  • 3) 169x4 – 9y4 4) x6 – y8
the sum and difference of two cubes
The Sum and Difference of Two Cubes
  • a3 + b3= (a + b)(a 2 – ab + b2)
  • a3 - b3= (a - b)(a 2 + ab + b2)
  • Examples:
  • 1) x3 + 125 2) z3 – 216
  • 3) 27m3 - bn3 4) 125x3 + 27y3
general factoring guidelines
General factoring guidelines
  • 1. Factor out a GCF if possible.
  • 2. If it’s a binomial, determine if it’s the sum or difference of two cubes or the difference of 2 squares. IF so, use the appropriate formula.
  • 3. If it’s a trinomial, use the guess-and-check method from sections 5.3 and 5.4.
  • 4. If it has 4 terms, try factoring by grouping.
  • 5. Always double check to see if your factors can be factored further.
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