  Let $H$ be a Hopf algebra over a field $K$ of characteristic $0$ and let $A$
be a bialgebra or Hopf algebra such that $H$ is isomorphic to a sub-Hopf
algebra of $A$ and there is an $H$-bilinear coalgebra projection $\pi$ from $A$
to $H$ which splits the inclusion. Then $A \cong R \#_\xi H$ where $R$ is the
pre-bialgebra of coinvariants. In this paper we study the deformations of $A$
by an $H$-bilinear cocycle. If $\gamma$ is a cocycle for $A$, then $\gamma$ can
be restricted to a cocycle $\gamma_R$ for $R$, and $A^\gamma \cong R^{\gamma_R}
\#_{\xi_\gamma} H$. As examples, we consider liftings of $\mathcal{B}(V) \#
K[\Gamma]$ where $\Gamma$ is a finite abelian group, $V$ is a quantum plane and
$\mathcal{B}(V)$ is its Nichols algebra, and explicitly construct the cocycle
which twists the Radford biproduct into the lifting.
