  We study the weak decays of exotic tetraquark states ${b\bar c}{q\bar q}$
with two heavy quarks. Under the SU(3) symmetry for light quarks, these
tetraquarks can be classified into an octet plus a singlet: $3\bigotimes\bar
3=1\bigoplus8$. We will concentrate on the octet tetraquarks with
$J^{P}=0^{+}$, and study their weak decays, both semileptonic and nonleptonic.
Hadron-level effective Hamiltonian is constructed according to the irreducible
representations of the SU(3) group. Expanding the Hamiltonian, we obtain the
decay amplitudes parameterized in terms of a few irreducible quantities. Based
on these amplitudes, relations for decay widths are derived, which can be
tested in future. We also give a list of golden channels that can be used to
look for these states at various colliders.
