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
${T_{r + 1}} = {\,^6}{C_r}{\left( {{x^2}} \right)^{6 - r}}{( - y)^r} = {( - 1)^r}{\,^6}{C_r}{x^{12 - 2r}}{y^r}$
Similar Questions
The middle term in the expansion of ${\left( {1 - \frac{1}{x}} \right)^n}\left( {1 - {x}} \right)^n$ in powers of $x$ is
The middle term in the expansion of ${\left( {1 - \frac{1}{x}} \right)^n}\left( {1 - {x}} \right)^n$ in powers of $x$ is
- [AIEEE 2012]
Find the term independent of $x$ in the expansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}$
Find the term independent of $x$ in the expansion of $\left(\frac{3}{2} x^{2}-\frac{1}{3 x}\right)^{6}$
The sum of the binomial coefficients of ${\left[ {2\,x\,\, + \,\,\frac{1}{x}} \right]^n}$ is equal to $256$ . The constant term in the expansion is
The sum of the binomial coefficients of ${\left[ {2\,x\,\, + \,\,\frac{1}{x}} \right]^n}$ is equal to $256$ . The constant term in the expansion is
The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is :-
The number of integral terms in the expansion of $(7^{1/3} + 11^{1/9})^{6561}$ is :-
Find an approximation of $(0.99)^{5}$ using the first three terms of its expansion.
Find an approximation of $(0.99)^{5}$ using the first three terms of its expansion.