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Q.
The determinant $\begin{vmatrix}x^2 & (y+z)^2 & y z \\ y^2 & (z+x)^2 & z x \\ z^2 & (x+y)^2 & x y\end{vmatrix}$ is divisible by:
Determinants
Solution:
Let $\Delta=\begin{vmatrix}x^2 & (y+z)^2 & y z \\ y^2 & (z+x)^2 & z x \\ z^2 & (x+y)^2 & x y\end{vmatrix}$
$C _2 \rightarrow C _2-2 C _3$
$\Delta=\begin{vmatrix}x^2 & y^2+z^2 & y z \\ y^2 & z^2+x^2 & z x \\ z^2 & x^2+y^2 & x y\end{vmatrix}$
$\Delta=\left(x^2+y^2+z^2\right)(x-y)(y-z)(z-x)(x+y+z)$