`|[a^(2), b^(2), c^(2)], [(a+1)^(2), (b+1)^(2), (c+1)^(2)], [(a-1)^(2), (b-1)^(2), (c-1)^(2)]| =-4(a-b)(b-c)(c-a)`

Explanation

To solve the determinant

\[
D = \begin{vmatrix}
a^2 & b^2 & c^2 \\
(a+1)^2 & (b+1)^2 & (c+1)^2 \\
(a-1)^2 & (b-1)^2 & (c-1)^2
\end{vmatrix}
...