How to Factor the Sum or Difference of Cubes Definition, Types, Examples & Uses

How to Factor the Sum or Difference of Cubes

Subject: Mathematics

Book: Maths Mastery

Sum of cubes a³ + b³ factors into (a + b)(a² – ab + b²), while difference of cubes a³ – b³ factors into (a – b)(a² + ab + b²). For instance, x³ – 8 = (x – 2)(x² + 2x + 4). These patterns appear frequently in polynomial algebra and advanced factorization tasks. You’ll see them in integral calculus (factoring integrands), economic models (cubic cost functions), and more. Knowing how to handle sums/differences of cubes fosters swift resolution of higher-order polynomial problems.