Question:
Write the general term in the expansion of $\left(x^{2}-y\right)^{6}$
Solution:
It is known that the general term $T_{r+1}\left\{\right.$ which is the $(r+1)^{\text {th }}$ 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 $\left(x^{2}-y^{6}\right)$ is
$T_{r+1}={ }^{6} C_{r}\left(x^{2}\right)^{6-r}(-y)^{r}=(-1)^{r}{ }^{6} C_{r} \cdot x^{12-2 r} \cdot y^{r}$