  Take $S \subset \mathrm{SL}_2(\mathbb{Z}) \times
\mathrm{SL}_2(\mathbb{Z})\times \mathrm{SL}_2(\mathbb{Z})$ be finite symmetric
and assume $S$ generates a group $G$ which is Zariski-dense in $\mathrm{SL}_2
\times \mathrm{SL}_2\times \mathrm{SL}_2(\mathbb{Z})$. This paper proves that
the Cayley graphs $$ \{\mathcal{C} a y(G(\bmod q), S(\bmod q))\}_{q \in
\mathbb{Z}_{+}} $$ form a family of expanders.
