  We present a framework for the computation of the Hopf 2-cocycles involved in
the deformations of Nichols algebras over semisimple Hopf algebras. We write
down a recurrence formula and investigate the extent of the connection with
invariant Hochschild cohomology in terms of exponentials.
  As an example, we present detailed computations leading to the explicit
description of the Hopf 2-cocycles involved in the deformations of a Nichols
algebra of Cartan type $A_2$ with $q=-1$, a.k.a. the positive part of the small
quantum group $\mathfrak{u}^+_{\sqrt{\text{-1}}}(\mathfrak{sl}_3)$. We show
that these cocycles are generically pure, that is they are not cohomologous to
exponentials of Hochschild 2-cocycles.
