\(\eqalign{
& 2{x^3}y - 2x{y^3} - 4x{y^2} - 2xy \cr
& = 2xy({x^2} - {y^2} - 2y - 1) \cr
& = 2xy\left[ {{x^2} - ({y^2} + 2y + 1)} \right] \cr
& = 2xy\left[ {{x^2} - {{\left( {y + 1} \right)}^2}} \right] \cr
& = 2xy\left[ {x + \left( {y + 1} \right)} \right].\left[ {x - \left( {y + 1} \right)} \right] \cr
& = 2xy\left( {x + y + 1} \right)\left( {x - y - 1} \right) \cr} \)
