Question

(a-b)^3+(b-c)^3+(c-a)^3​

Answer 1

Answer:

3(a-b)(b-c)(c-a)

Step-by-step explanation:

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

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

Answer 2

Answer:

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

Step-by-step explanation:

Given :

To evaluate the value of :

$(a-b)^3+(b-c)^3+(c-a)^3$

Solution :

We know that,

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

We know the identity,

if, $a + b + c = 0$

⇒ $a^3 + b^3 + c^3 = 3abc$

____

By replacing,

a with (a - b),

b with (b - c),

c with (c - a),

We get,

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