Question

Factorize:

(2x − 3y)³ + (4z − 2x)³ + (3y − 4z)³

Answer 1

(2x − 3y)³ + (4z − 2x)³ + (3y − 4z)³ 

Let 2x – 3y = a , 4z – 2x = b , 3y – 4z = c 

a + b + c= 3x − 2y + 2y − 4z + 4z − 3x = 0 

We know, a³ + b³ + c³ −3abc = (a + b + c)(a² + b² + c² − ab − bc − ca) 

⇒ a³ + b³ + c³ − 3abc = 0 

(2x − 3y)³ + (4z − 2x)³ + (3y − 4z)³ = 3(2x − 3y)(4z − 2x)(3y − 4z).