Is there an easy way to expand this determinant?

Question

I have this determinant and ask for an alternative way (not expanding way as we do always) to expand it:

$$\begin{vmatrix} y^2+z^2 &xy& xz\\ xy&x^2+y^2&yz \\ xz&yz&x^2+z^2 \end{vmatrix}$$

If you think the only way is to manipulate the elements by doing many many elementary operations, please comment me. I am aware of that method.

Answer 1

Using the Rule of Sarrus and factoring we obtain for the above matrix $A$ the determinant $$ \det(A)=x^2(y^2+z^2)^2. $$ This is without "many many elementary operation", but still by expanding, of course.

Edit: As Will has suggested, the above matrix should be just the square of the first matrix from the comments, and then the determinant is also the square.