Write the general term in the expansion of $\left(x^{2}-y\right)^{6}$
Write the general term in the expansion of $\left(x^{2}-y\right)^{6}$
It is known that the general term ${T_{r + 1}}{\rm{ \{ }}$ 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 $\left(x^{2}-y^{6}\right)$ is
${T_{r + 1}} = {\,^6}{C_r}{\left( {{x^2}} \right)^{6 - r}}{( - y)^r} = {( - 1)^r}{\,^6}{C_r}{x^{12 - 2r}}{y^r}$
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