(a^2+b^2-1)^2-4a^2b^2
=(a^2+b^2-1)^2-(2ab)^2
=(a^2+b^2-1-2ab)(a^2+b^2-1+2ab)
=[(a-b)^2-1][(a+b)^2-1]
=(a-b+1)(a-b-1)(a+b+1)(a+b-1)