Factoring Special Patterns

Sum of Cubes:x³ + y³ = (x + y) (x² - xy + y²)

Difference of Cubes:x³ - y³ = (x - y) (x² + xy + y²)

Example Factor the following polynomial: 64x³ + 125.

64x³ is (4x)³ and 125 is 5³, so this is a sum of cubes.

(x + y) (x² - xy + y²); x = 4x and y = 5

• Factor out the greatest common factor first, if possible.

• If the polynomial to be factored is a binomial, then it may be a difference of two squares, or a sum or difference of two cubes (remember that a sum of two squares does not factor).

• If the polynomial to be factored is a trinomial, then:
  
  • the polynomial may be a perfect square if two of the three terms are perfect squares.
  • the polynomial may be one of the general forms.

• If the polynomial to be factored consists of four or more terms, try factoring by grouping.

• Check if any of the factors can be factored further and do so when necessary.
• Finally, check the factoring by multiplying the factors to determine if they equal the original polynomial.