Question

factorise the following by using a suitable Identity (a-b)^3+(b-c)^3+(c-a)^3. it's urgent​

Answer 1

Answer:

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).