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

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

= xy(xy+ 1)+xy(x+ 1)+xy(y+ 1)+(x+ 1)+y

= xy(xy+ 1)+(xy+ 1)(x+ 1)+xy(y+ 1)+y

=(xy+ 1)(xy+x+ 1)+y(xy+x+ 1)

=(xy+x+ 1)(xy+y+ 1)