Edu Simulation

a³ + b³

Sum 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)