(a + b)³ = a³ + 3a²b + 3ab² + b³
(a+b)³ Proof
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Side lengths
a
= longer
b
= shorter
(a+b) = full side
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Piece types
■
a³ — 1 piece
■
a²b — 3 pieces
■
ab² — 3 pieces
■
b³ — 1 piece
a³ + 3a²b
+ 3ab² + b³
= (a+b)³
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📐 Derivation of (a+b)³
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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
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