  We compute liftings of the Nichols algebra of a Yetter-Drinfeld module of
Cartan type $B_2$ subject to the small restriction that the diagonal elements
of the braiding matrix are primitive $n$th roots of 1 with odd $n\neq 5$. As
well, we compute the liftings of a Nichols algebra of Cartan type $A_2$ if the
diagonal elements of the braiding matrix are cube roots of 1; this case was not
completely covered in previous work of Andruskiewitsch and Schneider. We study
the problem of when the liftings of a given Nichols algebra are
quasi-isomorphic. The Appendix (with I. Rutherford) contains a generalization
of the quantum binomial formula. This formula was used in the computation of
liftings of type $B_2$ but is also of interest independent of these results.
