x^2y^2+x^2y+xy^2+3xy+x+y+1
=x^2y^2+2xy+1+x^2y+xy^2+xy+x+y
=(xy+1)^2+xy(x+y)+xy+(x+y)
=(xy+1)^2+(xy+1)(x+y)+xy
=(xy+1+x)(xy+1+y)