Question

If (a-b)³ +(b-c)³ +(c-a)^3is simplified then the answer is​

Answer 1

Answer:

(a-b)³ +(b-c)³ +(c-a)³

=> 3(a²b + ab² + b²c + bc² + a²c + ac²)

Answer 2

Answer:

3a

2

(c−b)+3b

2

(a−c)+3c

2

(b−a)

We know, (a−b)

3

=a

3

−b

3

−3a

2

b+3ab

2

⟹ (a−b)

3

=a

3

−b

3

−3ab(a−b).

Then,

(a−b)

3

+(b−c)

3

+(c−a)

3

=(a

3

−3a

2

b+3ab

2

−b

3

)+(b

3

−3b

2

c+3bc

2

−c

3

)+(c

3

−3c

2

a+3ca

2

−a

3

)

=−3a

2

b+3ab

2

−3b

2

c+3bc

2

−3c

2

a+3ca

2

=3a

2

(c−b)+3b

2

(a−c)+3c

2

(b−a).