Edu Simulation

a³ − b³

Difference of Cubes · Interactive Explorer

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Formula

Full derivation and simplified identity for a³ − b³

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Solve

Step-by-step guided questions to factor expressions

Step-by-step derivation

start (a − b)³ = a³ − b³ − 3ab(a − b)

or, (a − b)³ + 3ab(a − b) = a³ − b³

or, (a − b)(a − b)² + 3ab(a − b) = a³ − b³

or, (a − b){(a − b)² + 3ab} = a³ − b³ ∵ (a − b) is common on both

or, (a − b)(a² − 2ab + b² + 3ab) = a³ − b³ ∵ using formula of (a − b)²

or, (a − b)(a² + ab + b²) = a³ − b³

Simplified identities

(i) a³ − b³ = (a − b)³ + 3ab(a − b)

(ii) a³ − b³ = (a − b)(a² + ab + b²)