x^2+4xy+2x+3y^2+6y
⇔ (3xy + 3y² + 6y) + (x² + 2x + xy)

⇔ 3y(y + x + 2) + x(x + y + 2)

⇔ (x + 3y) + (x + 2 + y)

x2−x−xy−2y2+2yx2-x-xy-2y2+2y

⇔x2−x+xy−2xy−2y2+2y⇔x2-x+xy-2xy-2y2+2y

⇔(x2−x+xy)−(2xy+2y2−2y)⇔(x2-x+xy)-(2xy+2y2-2y)

⇔x(x−1+y)−2y(x+y−1)⇔x(x-1+y)-2y(x+y-1)

⇔(x−2y)(x+y−1)