解: (x^2+y^2)^2-(1+2xy)^2
=x^4+2x^2y^2+y^4-1-4xy-4x^2y^2
=x^2-2x^2y^2+y^4-1
=(x^2-y^2)^2-1
=(x^2-y^2+1)(x^2-y^2-1)