a^2-b^2+4a+2b+3
＝（a^2+4a+4）-(b^2-2b+1)
=(a+2)^2-(b-1)^2
=(a+2+b-1)(a+2-b+1)
=(a+b+1)(a-b+3)
x^2-2x-2y^2+4y-xy
=(x^2-xy-2y^2)-(2x-4y)
=(x-2y)(x+y)-2(x-2y)
=(x-2y)(x+y-2)
x(x-1)+y(y+1)-2xy
=x^2-x+y^2+y-2xy
=x^2+y^2-2xy-(x-y)
=(x-y)^2-(x-y)
=(x-y)(x-y-1)