Question

Factorize: a³ − 3a²b + 3ab² − b³ + 8

Answer 1

a³ − 3a²b + 3ab² − b³ + 8 

Using: a³ − b³ − 3a²b + 3ab² = (a−b)³ 

= (a−b)³ + 2³ 

Again , Using: a³ + b³ =(a + b)(a² – ab + b²)] 

=(a−b+2)((a−b)²−(a−b)² + 2²) 

= (a−b+2)(a²+b²−2ab−2(a−b)+4) 

= (a−b+2)(a²+b²−2ab−2a+2b+4) 

a³ − 3a²b + 3ab² − b³ + 8 = (a−b+2)(a²+b²−2ab−2a+2b+4)