a) 0
b) 1
c) 2
d) 3
correct answer is: a) 0
Formula use: a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
Explanation
Here, given expression is :
\left(a-b\right)\left(a^2+ab+b^2\right)+\left(b-c\right)\left(b^2+bc+c^2\right)+\left(c-a\right)\left(c^2+ca+a^2\right)
\rightarrow\left(a^3-b^3\right)+\left(b^3-c^3\right)+\left(c^3-a^3\right)
\rightarrow a^3-b^3+b^3-c^3+c^3-a^3
\therefore 0
Ans: 0.