Question

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

Answer 1

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 $(x^2-yx{)}^{12}$ is
$T_{r+1}{=}^{12}{C}_r\left(x^2{)}^{12-x}\right(-yx{)}^r=(-1{)}^{r}12C_r.x^{24-2r}.y^r.x^r=(-1{)}^{r}12C_r.x^{24-r}.y^r$