  In this paper, we construct the bilinear identities for the wave functions of
an extended Kadomtsev-Petviashvili (KP) hierarchy, which is the KP hierarchy
with particular extended flows (2008, Phys. Lett. A, 372: 3819). By introducing
an auxiliary parameter (denoted by $z$), whose flow corresponds to the
so-called squared eigenfunction symmetry of KP hierarchy, we find the
tau-function for this extended KP hierarchy. It is shown that the bilinear
identities will generate all the Hirota's bilinear equations for the
zero-curvature forms of the extended KP hierarchy, which includes two types of
KP equation with self-consistent sources (KPSCS). It seems that the Hirota's
bilinear equations obtained in this paper for KPSCS are in a simpler form by
comparing with the results by Hu and Wang (2007, Inverse Problems, 23: 1433).
