How to write this as a multiplication: $4 x^2 y^2 - (x^2 + y^2 - z^2)^2$?

$$ \begin{align} \color{magenta}{4 x^2 y^2 - (x^2 + y^2 - z^2)^2} & = \color{brown}{(2xy +x^2+y^2-z^2)(2xy -x^2-y^2+z^2)} \\ &= \color{blue}{((x+y)^2-z^2)(-(x-y)^2 -z^2)}\\ & = \boxed{\color{red}{-(x+y+z)(x+y-z)(x-y-z)(x-y+z)}} \end {align}$$