Without expanding show that `|[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2b^2,a b ,a+b]|=0`

Explanation

To show that the determinant

\[
D = \begin{vmatrix}
b^2c^2 & bc & b+c \\
c^2a^2 & ca & c+a \\
a^2b^2 & ab & a+b
\end{vmatrix} = 0
...