(x+y)(x-y)+4(y-1)x^2y^2-4xy-x^2-y^2+1

(x+y)(x-y)+4(y-1)x^2y^2-4xy-x^2-y^2+1
(x+y)(x-y)+4(y-1)
x^2y^2-4xy-x^2-y^2+1

(x+y)(x-y)+4(y-1)x^2y^2-4xy-x^2-y^2+1
(x+y)(x-y)+4(y-1)
=x²-y²+4y-4
=x²-(y²-4y+4)
=x²-(y-2)²
=[x-(y-2)][x+(y-2)]
=(x-y+2)(x+y-2)
x²y²-4xy-x²-y²+1
=(x²y²-2xy+1)-(x²+2xy+y²)
=(xy-1)²-(x+y)²
=[(xy-1)+(x+y)][(xy-1)-(x+y)]
=(xy+x+y-1)(xy-x-y-1)

(x+y-2)(x-y+2)
(xy-1+x+y)(xy-1-x-y)

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

x^2-(y-2)^2
(x^2-1)(y^2-1)-4xy