The expression `(a-b)^3+\ (b-c)^3+\ (c-a)^3` can be factorized as (a)`(a-b)(b-c)(c-a)` (b) `3(a-b)(b-c)(c-a)` (c)`-3\ (a-b)(b-c)(c-a)` (d)`(a+b+c)(a^2+b^2+c^2-a b-b c-c a)`

Explanation

`(a-b)^3+\ (b-c)^3+\ (c-a)^3`
Expand the terms:
`=(a^3-3a^2b+3ab^2-b^3)+(b^3-3b^2c+3bc^2-c^3)+(c^3-3c^2a+3ca^2-a^3)`
`=-3a^2b+3ab^2-3b^2c+3bc^2-3c^2a+3ca^2`
`=3(-a^2b+ab^2-b^2c+bc^2-c^2a+ca^2)`
`=3(-a^2b+ab^2-b^2c+bc^2-c^2a+ca^2+bac-abc)`
`=3[(c-a)\(ab-ac-b^2+bc)]`
`=3(c-a)\(b-c)\(a-b)`
Therefore, option B is correct