Consider the determinant with elements:
$a_{11} = ax-by-cz, a_{12}=ay+cz, a_{13}=cx+az$ $a_{21}=ay+bx, a_{22}=by-cz-ax, a_{23}=bz+cy$ $a_{31}=cx+az, a_{32}=bz+cy, a_{33}=cz-ax-by$
Where $a_{ij}$ represents the element in the $i^{th}$ row and $j^{th}$ column.
I started out with 2 empty $3X3$ determinants to factorize this. The first row of the second determinant was filled as $a(1,1)=x, a(1,2)=y, a(1,3)=z$ and first row of the first determinant was filled as $a(1,1)=a,a(2,1)=b,a(3,1)=c$. I am not finding a good continuation to find the solution to the problem. Also, how do I improve my matrix/determinant factorizing skills? It takes me quite a while to fill in 2 empty determinants to get the original one as the product. Especially when it comes to problems like these where factor theorem cannot be easily applied. Any advice will be appreciated.