  Using elementary means, we derive the three most popular splittings of
$e^{(A+B)}$ and their error bounds in the case when $A$ and $B$ are (possibly
unbounded) operators in a Hilbert space, generating strongly continuous
semigroups, $e^{tA}$, $e^{tB}$ and $e^{t(A+B)}$. The error of these splittings
is bounded in terms of the norm of the commutators $[A, B]$, $[A, [A, B]]$ and
$[B, [A, B]]$.
