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

$$ 4 x^2 y^2 - (x^2 + y^2 - z^2)^2$$

(which comes up, for example, in computing the area of a triangle using the cosine law).
I would like to convert this to a product.
Wolfram tells me it's

$$ -(x - y - z) (x + y - z) (x - y + z) (x + y + z)$$

How can I find this form if I don't already know it? What operations should I perform?

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