`P = 2. (x + y). (x - y) - (x - y)^2 + (x + y)^2 - 4y^2`
`= (2x + 2y). (x - y) - (x^2 - 2xy + y^2) + (x^2 + 2xy + y^2) - 4y^2`
`= (2x^2 + 2xy - 2xy - 2y^2) - x^2 + 2xy - y^2 + x^2 + 2xy + y^2 - 4y^2`
`= 2x^2 - 2y^2 - x^2 + 2xy - y^2 + x^2 + 2xy + y^2 - 4y^2`
`= (2x^2 - x^2 + x^2) - (2y^2 + y^2 - y^2 + 4y^2) + (2xy + 2xy)`
`= 2x^2 - 6y^2 + 4xy`