Formula

a³ + b³ Formula — Sum of Cubes, Proof, Examples

The a cube plus b cube formula — $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ — factors the sum of two cubes into a binomial times a trinomial. This article gives the formula, its algebraic proof, three worked examples at three difficulty tiers, a side-by-side with $a^3 - b^3$, the common factoring slips, and where the identity shows up in engineering and physics.