[tex](-4z^3-2z+8)-(4z^3+3^2-5)\\\\=-4z^3-2z+8-4z^3-3^2-(-5)\\\\=-4z^3-2z+8-4z^3-9+5\\\\\text{combine like terms}\\\\=(-4z^3-4z^3)-2z+(8-9+5)\\\\=\boxed{-8z^3-2z+4}[/tex]
