ID006 · Algebraic identities · Classes 9–10
a³ + b³
A sum of two cubes factorises into (a + b) times a quadratic factor.
a³ + b³a³ + b³
📐 Formula
a³ + b³ = (a + b)(a² − ab + b²)
✏️ Worked example
3³ + 2³ = 27 + 8 = 35 = (3 + 2)(9 − 6 + 4) = 5 × 7.
🌍 Where it is used
Factorising cubic expressions.
❓ Quick check
x³ + 8 = ?
🏋️ Practice
EasyFactorise x³ + 1.
Answer: (x + 1)(x² − x + 1)
MediumFactorise 27 + y³.
Answer: (3 + y)(9 − 3y + y²)
ChallengeEvaluate 4³ + 1³ using the identity.
Answer: 5 × 13 = 65