(a + b)³ = a³ + 3a²b + 3ab² + b³

(a+b)³ Proof

Side lengths
a = longer
b = shorter
(a+b) = full side
Speed:
Piece types
a³ — 1 piece
a²b — 3 pieces
ab² — 3 pieces
b³ — 1 piece
a³ + 3a²b
+ 3ab² + b³
= (a+b)³
 

🧮 (a+b)³ Step-by-Step Practice

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📐 Derivation of (a+b)³

The big cube of side (a+b) is cut into 8 pieces.
Adding all volumes:
(a+b)³ = a³ + a²b + a²b + a²b + ab² + ab² + ab² + b³

👆 Click any step to expand it