Do the grouping $z^{2}ty+z^{2}t-2y-2=\left(z^{2}ty+z^{2}t\right)+\left(-2y-2\right)$, and factor out $tz^{2}$ in the first and $-2$ in the second group.
$$tz^{2}\left(y+1\right)-2\left(y+1\right)$$
Factor out common term $y+1$ by using distributive property.
