Question

Factorize each of the following expressions:
(a-3b)3+(3b-c)3+(c-a)3

Answer 1

The algebraic expression is given as : (a - 3b)³ + (3b - c)³ + (c - a)³

Let (a - 3b) = a , (3b - c) = b , (c - a) = c. Then  

a + b + c =  a - 3b + 3b - c + c - a = 0

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

∴ a³ + b³ + c³ =  3abc

⇒  (a - 3b)³ + (3b - c)³ + (c - a)³ = 3(a - 3b) (3b - c)(c - a)

HOPE THIS ANSWER WILL HELP YOU…..

Similar questions :

Factorize each of the following expressions:

(2x-3y)³+(4z-2x)³+(3y-4z)³

https://brainly.in/question/15902457

Factorize:

8x³+27y³+36x² y+54xy²

https://brainly.in/question/15901889

Answer 2

Answer:

Step-by-step explanation:

Let (a - 3b) = a , (3b - c) = b , (c - a) = c. Then  

a + b + c =  a - 3b + 3b - c + c - a = 0

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

∴ a³ + b³ + c³ =  3abc

⇒  (a - 3b)³ + (3b - c)³ + (c - a)³ = 3(a - 3b) (3b - c)(c - a)