Question

Write the general term in the expansion of $(x^2-y{)}^6$

Answer 1

It is known that the general term $(T{)}_{r+1}$ {which is the $(r+1)$ 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 $(x^2-y{)}^6$ is

$T_{r+1}{=}^6{C}_r\left(x^2{)}^{6-r}\right(-y{)}^r=(-1{)}^{r}6C_r{x}^{12-2r}{y}^r$