Factoring

Factoring cubics

Sum and Difference of Cubes

Sum of cubes:

\[a^3 + b^3 = (a+b)(a^2 - ab + b^2)\]

Difference of cubes:

\[a^3 - b^3 = (a-b)(a^2 +ab + b^2)\]

Note that in both cases

  • the first operation on the right side is the same as the operation on the left side
  • the second operation on the right side is the opposite of the operation on the left side
  • the third operation on the right side is always $+$