  We extend recent work by Howie, Mathews and Purcell to simplify the
calculation of A-polynomials for any family of hyperbolic knots related by
twisting. The main result follows from the observation that equations defining
the deformation variety that correspond to the twisting are reminiscent of
exchange relations in a cluster algebra. We prove two additional results with
analogues in the context of cluster algebras: the Laurent phenomenon, and
intersection numbers appearing as exponents in the denominator. We demonstrate
our results on the twist knots, and on a family of twisted torus knots for
which A-polynomials have not previously been calculated.
