what is the decomposition of $(x^2+y^2+z^2)(x+y+z)(x+y-z)(-x+y+z)(x-y+z)-8x^2y^2z^2$? I want to have a decomposition of this :
$$(x^2+y^2+z^2)(x+y+z)(x+y-z)(-x+y+z)(x-y+z)-8x^2y^2z^2$$
I have tried all possible calculation which came to my mind,I will describe one of it which is better but no result:
I put $(x+y-z)=a$ ,$ (-x+y+z)=b$ and $(x-y+z)=c$ and we have $(x+y+z)=a+b+c$ so we have $$(x^2+y^2+z^2)(a+b+c)abc-8x^2y^2z^2$$
but I couldn't make it simpler, it will be great if you help me about it,thanks.

Maple does the job by
factor(expand((x^2+y^2+z^2)*(x+y+z)*(x+y-z)*(-x+y+z)*(x-y+z)-8*x^2*y^2*z^2));

$$ - \left( {x}^{2}-{y}^{2}-{z}^{2} \right)  \left( {x}^{2}+{y}^{2}-{z}^{
2} \right)  \left( {x}^{2}-{y}^{2}+{z}^{2} \right) 
 .$$
