A new expansion formula in series of a general class of q-polynomials is proved here for a multivariable function which is defined by a muliple power series with essentially arbitrary terms. This new result provides an interesting unification (and generalization) of several classes of q- polynomial expansions given earlier by the second author [Inst. Math. Am. J. Appl. Math. 30, 315-323 (1983; Zbl 0504.33003); ibid. 33, 205-209 (1984; Zbl 0533.33001)]. It can also be applied to derive a number of polynomial expansions and multiplication theorems for various q- hypergeometric functions of one and more variables. Some of these applications leading to bilinear formulas for such q-orthogonal polynomials as the (little) q-Jacobi, q-Laguerre, and q-Hahn polynomials, and to various summation (or multiplication) formulas for q-Lauricella functions, are considered.