Using a temperature, density, isospin and momentum dependent equation of state of nuclear matter obtained within the framework of Extended Skryme Hartree Fock theory, we study the chemical and mechanical instabilities of nuclear matter at different temperatures, density and relative neutron excess,and compare them with the results of the simplified three-parameter potentials, namely soft and hard potentials in which the symmetry energy part is added by hand. It is found that the asymmetric nuclear matter has remarkable chemical instability in the mechanically stable region. The relationship between the mechanical and chemical instabilities is different from the result of soft and hard potentials, which is shown to result from the difference of the density dependence form of single particle potentials. We also provide the chemical and mechanical spinodal regions in pressure density plane, and their isospin dependence is discussed. In particular, the behaviours of chemical instability around the critical temperature and the possible consequences in heavy ion collisions at intermediate energy are investigated.