a)
[tex]-(x+1)+(2x+4)=\\\\=-x-1+2x+4=\\\\=-x+2x-1+4=\boxed{x+3}[/tex]
b)
[tex](x+4)+(2x-6)=\\\\=x+4+2x-6=\\\\=x+2x+4-6=\boxed{3x-2}[/tex]
c)
[tex]-(2y+3x)+(-4y+2x+1)=\\\\=-2y-3x-4y+2x+1=\\\\=-3x+2x-2y-4y+1=\boxed{-x-6y+1}[/tex]
d)
[tex]-(x-2xy)-(4x+xy)+(xy-x)=\\\\=-x+2xy-4x-xy+xy-x=\\\\=-x-4x-x+2xy-xy+xy=\boxed{-6x+2xy}[/tex]
e)
[tex](x^2+2x+1)-(x^2-4x+3)=\\\\=x^2+2x+1-x^2+4x-3=\\\\=x^2-x^2+2x+4x+1-3=\boxed{6x-2}[/tex]
