Using the property of determinants and without expanding, prove that:`|[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b, c(a+b)]|=0`

Explanation

To prove that the determinant

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