In this paper, we determine the general solution of the functional equations f ( x + y + x y ) = p ( x ) + q ( y ) + g ( x ) h ( y ) ,           ( ∀ x , y ∈ ℜ * ) and f ( a x + b y + c x y ) = f ( x ) + f ( y ) + f ( x ) f ( y ) ,           ( ∀ x , y ∈ ℜ ) which are generalizations of a functional equation studied by Pompeiu. We present a method which is simple and direct to determine the general solutions of the above equations without any regularity assumptions.