I know this property well : $$\begin{vmatrix} 1 & x & x^2 +a \\ 1 & y & y^2+b \\ 1 & z & z^2+c \\ \end{vmatrix} = \begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{vmatrix} + \begin{vmatrix} 1 & x & a \\ 1 & y & b \\ 1 & z & c \\ \end{vmatrix}. $$
But the question I am unable to find answer to is This applies to two rows or column at a time Like $$ \begin{vmatrix} 1+a & x+b & x^2+c \\ 1+d & y+e & y^2+f \\ 1+g & z+h & z^2+i \\ \end{vmatrix} $$
to simplify to $$ \begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{vmatrix} + \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \\ \end{vmatrix}. $$
If it does to two even rows please mention