ID005 · Algebraic identities · Classes 9–10
(a − b)³
The cube of a difference is what remains of an a-cube when slabs of thickness b are removed from three faces.
(a−b)³(a − b)³
📐 Formula
(a − b)³ = a³ − 3a²b + 3ab² − b³
✏️ Worked example
(4 − 1)³ = 64 − 48 + 12 − 1 = 27.
🌍 Where it is used
Fast cubing: 99³ = (100 − 1)³.
❓ Quick check
(x − 1)³ = ?
🏋️ Practice
Easy(3 − 1)³ = ?
Answer: 8
MediumExpand (x − 2)³.
Answer: x³ − 6x² + 12x − 8
ChallengeFind 9³ using (10 − 1)³.
Answer: 1000 − 300 + 30 − 1 = 729