Question

(a-b)³+(b-c)³+ (c-a)³=
A. (a+b+ c) (a²+b² + c²-ab-bc-ca)
B. (a-b)(b-c) (c-a)
C. 3 (a-b)(b-c) (c-a)
D. none of these

Answer 1

Given : (a - b)³ + (b - c)³ + (c - a)³

 

Solution :  

Let (a - b) = p ,  (b - c) = q and (c - a) = r

p + q + r = 0

(a - b) + (b - c) + (c - a) = 0

We know that if,  a + b + c = 0, then a³ + b³ + c³ = 3abc

Now,

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

Hence the value of (a - b)³ + (b - c)³ + (c - a)³ = 3(a - b) (b - c) (c - a).

Among the given options option (C) 3(a - b) (b - c) (c - a)  is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

Some questions of this chapter :

If a + b + c = 0, then write the value of a³+b³+c³.

https://brainly.in/question/15902765

 

Write the value of: (1/2)³ + (1/3)³ - (5/6)³

brainly.in/question/15902770

Answer 2

$\huge{ \red{Given : -}}$

(a+b)³ + (b-c)³ + (c-a)³

= a³ - b³ - 3a²b + 3ab² + b³ - c³ - 3b² 0 + 37c³ + c³ + a³ - 3c² a + 3ca²

= -3a²b + 3ab² - 3a²c + 3bc² - 3c²a + 3ac²

= 3ab (-a + b) + abc (- b+ c) + 3ca (-c + a)

Answer : - C. 3 (a-b)(b-c) (c-a)