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