$\begin{vmatrix} 1 &x &x^{2} \\ 1 & y& y^{2}\\ 1& z& z^{2} \end{vmatrix}$
$(B):$ $C2\rightarrow C2+C1 ,\ C3\rightarrow C3+C1$
$\begin{vmatrix} 1 &x+1 &x^{2}+1 \\ 1 & y+1& y^{2}+1\\ 1& z+1& z^{2}+1 \end{vmatrix}$
$(C):$ $R1\rightarrow R1-R2 ,\ R2\rightarrow R3-R2$
$\begin{vmatrix} 0 &x-y &x^{2}-y^{2} \\ 0 & y-z& y^{2}-z^{2}\\ 1& z& z^{2} \end{vmatrix}$
$(D):$ $R1\rightarrow R1+R2 ,\ R2\rightarrow R3+R2$
$\begin{vmatrix} 2 &x+y &x^{2}+y^{2} \\ 2 & y+z& y^{2}+z^{2}\\ 1& z& z^{2} \end{vmatrix}$
We can't get option(A) from given Determinant.
Hence,Option(A) is the correct choice.