Question

If a − 2b = 4, ab = 6, find a³ − 8b³.

Answer 1

Here, a − 2b = 4, ab = 6,

Using the identity

a³ − (2b)³ = (a − 2b) (a² + 2ab + 4b²) and

a² + 2ab + 4b² = (a − 2b)² + 6ab,   ...[Used (a − b)³ = a³ − 3a²b + 3ab² − b³]

Hence, we get,

a³ − 8b³ = (a − 2b) [(a − 2b)² + 6ab]

= 4 [(4)² + 6(6)]

= 4 [16 + 36]

= 4(52)

∴ a³ − 8b³ = 208