  A simple method is proposed for deforming $A_\infty$-algebras by means of the
resolution technique. The method is then applied to the associative algebras of
polynomial functions on quantum superspaces. Specifically, by introducing
suitable resolutions, we construct explicit deformations of these algebras in
the category of minimal $A_\infty$-algebras. The relation of these deformations
to higher spin gravities is briefly discussed.
