Question

Find : (a - b)(a - b)(a - b)

Answer 1

(a + b)(a + b)(a + b)
= (a × a + a × b + b × a + b × b)(a + b)
= (a² + ab + ab + b²)(a + b)
= (a² + b² + 2ab)(a + b)
= a² × a + a² × b + b² × a + b² × b + 2ab × a + 2ab × b
= a³ + a² b + ab² + b³ + 2a²b + 2ab²
= a³ + b³ + 3a²b + 3ab²

replacing b by -b, we get
= a³ + (-b)³ + 3a²(-b) + 3a(-b)²
= a³ - b³ - 3a²b + 3ab²