Factorization Of Algebraic Expressions — Maths STD 9 — Question

By we know that $a^3+b^3+c^3-3 a b c=(a+b+c)\left(a^2+b^2+c^2-a b-b c-c a\right)$
If $a+b+c=0$, then
$a^3+b^3+c^3=3 a b c$
In given expression,
Let $\mathrm{a}-\mathrm{b}=\mathrm{A}, \mathrm{b}-\mathrm{c}=\mathrm{B}, \mathrm{c}-\mathrm{a}=\mathrm{C}$
Now, $a-b+b-c+c-a=0$
i.e. $A+B+C=0$
$\Rightarrow A^3+B^3+C^3=3 A B C$
$\Rightarrow(a-b)^3+(b-c)^3+(c-a)^3=3(a-b)(b-c)(c-a)$
Hence, correct option is $(b)$.