Factor $(x^2+y^2-z^2)^2-4x^2y^2$ as the product of four polynomials of degree $1$, each of which has a positive coefficient of $x$?
Thanks for the help
Factor (x2 + y2 - z2)2 - 4x2y2
---> (x2 + y2 - z2)2 - (2xy)2
Factor as the difference of two squares:
---> [ ( x2 + y2 - z2 ) + (2xy) ] · [ ( x2 + y2 - z2 ) - (2xy) ]
Rewrite:
---> [ x2 + 2xy + y2 - z2 ] · [ x2 - 2xy + y2 - z2 ]
Factor:
---> [ (x + y)2 - z2 ] · [ (x - y)2 - z2 ]
Factor as the difference of two squares:
---> [ (x + y + z)(x + y - z) ] · [ (x - y + z)(z - y - z) ]
Answer: (x + y + z)(x + y - z)(x - y + z)(z - y - z)