(a − b)³ = a³ − 3a²b + 3ab² − b³

(a−b)³ Proof

Side lengths
a = longer
b = shorter
(a−b) = inner side
Speed:
Piece types
■ (a−b)³ — 1 piece
■ (a−b)²b — 3 pieces
■ (a−b)b² — 3 pieces
■ b³ — 1 piece
a³ = (a−b)³
+ 3(a−b)²b
+ 3(a−b)b²
+ b³
 

🧮 Step-by-Step Practice

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📐 Derivation of (a−b)³

We know a³ = volume of big cube with side a.
We cut it into 8 pieces. So:
a³ = (a−b)³ + b³ + (a−b)²·b + (a−b)²·b + (a−b)²·b + (a−b)b² + (a−b)b² + (a−b)b²

👆 Click any step to expand it