The value of `[(a-b)(b-c)(c-a)]` is equal to

Options

A. 0
B. 1
C. 2[ a b c ]
D. 2

Answer

A

Explanation

Now, `[(a-b)(b-c)(c-a)]`
`= (a-b).[(b-c) xx (c-a)]`
`= (a-b).[bxxc-bxxa-cxxc+cxxa]`
`= (a-b).[bxxc-bxxa+cxxa] " "[ :' c xx c = 0]`
`= a.[bxxc]- a.[bxxa] + a.[cxxa] - b.[bxxc]+b.[bxxa] - b.[cxxa]`
`= [abc] - 0 + 0 + 0 - [bca]`
`= [abc] - [abc] = 0`