We investigate freely expanding liquid sheets made of either simple Newtonian fluids or solutions of high molecular water-soluble polymer chains. A sheet is produced by the impact of a drop on a quartz plate covered with a thin layer of liquid nitrogen that suppresses shear viscous dissipation thanks to an inverse Leidenfrost effect. The sheet expands radially until reaching a maximum diameter and subsequently recedes. Experiments indicate the presence of two expansion regimes: the capillary regime, where the maximum expansion is controlled by surface tension forces and does not depend on the viscosity, and the viscous regime, where the expansion is reduced with increasing viscosity. In the viscous regime, the sheet expansion for polymeric samples is strongly enhanced as compared to that of Newtonian samples with comparable zero-shear viscosity. We show that data for Newtonian and non-Newtonian fluids collapse on a unique master curve where the maximum expansion factor is plotted against the relevant effective \textit{biaxial extensional} Ohnesorge number that depends on fluid density, surface tension and the biaxial extensional viscosity. For Newtonian fluids, this biaxial extensional viscosity is six times the shear viscosity. By contrast, for the non-Newtonian fluids, a characteristic \textit{Weissenberg number}-dependent biaxial extensional viscosity is identified, which is in quantitative agreement with experimental and theoretical results reported in the literature for biaxial extensional flows of polymeric liquids.