How do you factor: 2x^2+ xy- y^2+ 3x+ 1

2x^2+ xy- y^2+ 3x+1= 

(2x-y)(x+y)+3x+1= 

(2x-y)(x+y)+2x+x+1= 

(2x-y)(x+y)+(2x-y)+(x+y+1)= 
(2x-y)(x+y+1)+(x+y+1)= 

(2x-y+1)(x+y+1) 


:)