  The aim of this article is to give a method to construct bimodule resolutions
of associative algebras, generalizing Bardzell's well-known resolution of
monomial algebras. We stress that this method leads to concrete computations,
providing thus a useful tool for computing invariants associated to the
algebras. We illustrate how to use it giving several examples in the last
section of the article. In particular we give necessary and sufficient
conditions for noetherian down-up algebras to be 3-Calabi-Yau.
