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

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Solution

It is known that the general term $T_{r + 1}$ which is the $(r + 1)$ th term in
the binomial expansion of $(a + b)^{n}$ is given by $T_{r + 1} =^{n} C_{r} a^{n - r} b^{r}$
Thus, the general term in the expansion of $(x^{2} - y x)^{12}$ is
$T_{r + 1} =^{12} C_{r} (x^{2})^{12 - x} (- y x)^{r} = (- 1)^{r} 12 C_{r} . x^{24 - 2 r} . y^{r} . x^{r} = (- 1)^{r} 12 C_{r} . x^{24 - r} . y^{r}$

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