Question

factorisation question here

Answer 1

Answer:

(a) (x - 1)(x² + x + 1)

Step-by-step explanation:

Short Method :

As a³ - b³ = (a - b)(a² + ab + b²)

=> x³ - 1 = x³ - 1³

Here a = x, b = 1

Hence x³ - 1 = (x - 1)(x² + x + 1)

Derivation :

(a - b)³ = a³ - b³ - 3a²b + 3ab²

[ Tip : (a - b)³ = (a - b)(a - b)² ]

=> (a - b)³ = a³ - b³ - 3ab(a - b)

=> (a - b)³ + 3ab(a - b) = a³ - b³

=> a³ - b³ = (a - b){(a - b)² + 3ab}

=> a³ - b³ = (a - b)(a² - 2ab + b² + 3ab)

Hence a³ - b³ = (a - b)(a² + ab + b²).

Coming back, Option (a) Is the correct answer.

Thanks !