If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are :
(1) `(a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab`
(3) `a^(2)-b^(2)=(a+b)(a-b)`
(4) `(a+b)^(3)=a^(3)+b^(3)+3ab(a+b)`
(6) `a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab)`
(8) `(a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c))`
(10) `a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca)`
`=1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)]`
`If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc`
If a,b, c are real and distinct numbers, then the value of `((a-b)^(3)+(b-c)^(3)+(c-a)^(3))/((a-b).(b-c).(c-a))is `

Options

A. 1
B. 2
C. 3
D. 4