Without expanding, show that the value of each of the determinants is zero: `|[1,a, a^2-bc],[1,b,b^2-ac],[1,c,c^2-ab]|`

Explanation

$$
\left|\begin{array}{lll}
1 & a & a^{2}-b c \\
1 & b & b^{2}-c a \\
1 & c & c^{2}-a b
\end{array}\right|=\left|\begin{array}{ccc}
1 & a & a^{2} \\
1 & b & b^{2} \\
...