Evaluate:
Question:

Evaluate:

$\left|\begin{array}{lll}a & b & c \\ c & a & b \\ b & c & a\end{array}\right|$

Solution:

$\Delta=\left|\begin{array}{lll}a & b & c \\ c & a & b \\ b & c & a\end{array}\right|$

$=a\left(a^{2}-b c\right)-b\left(c a-b^{2}\right)+c\left(c^{2}-b a\right)$

$=a^{3}-a b c-b c a+b^{3}+c^{3}-a b c$

$=a^{3}+b^{3}+c^{3}-3 a b c=(a+b+c)\left(a^{2}+b^{2}+c^{2}-a b-b c-c a\right)$

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