Write the general term in the expansion of $(x^{2}-yx)^{12}, x \neq 0$.

The general term $T_{r+1}$ in the binomial expansion of $(a+b)^{n}$ is given by $T_{r+1} = {}^{n}C_{r} a^{n-r} b^{r}$.
For the expansion of $(x^{2}-yx)^{12}$,we have $a = x^{2}$,$b = -yx$,and $n = 12$.
Substituting these values into the formula:
$T_{r+1} = {}^{12}C_{r} (x^{2})^{12-r} (-yx)^{r}$
$T_{r+1} = {}^{12}C_{r} (x^{24-2r}) (-1)^{r} y^{r} x^{r}$
$T_{r+1} = (-1)^{r} {}^{12}C_{r} x^{24-2r+r} y^{r}$
$T_{r+1} = (-1)^{r} {}^{12}C_{r} x^{24-r} y^{r}$