Question

Find the $4^{th}$ term in the expansion of $(x-2y{)}^{12}$.

Answer 1

Here general term in the expansion of $(x-2y{)}^{12}$ is

$T_{r+1}={12}_{C_r}(x{)}^{12-r}.(-2y{)}^r$

$=(-1{)}^r{12}_{C_r}{2}^r.x^{12-r}.y^r$

Putting r=3,

$\therefore T_4=(-1{)}^3{12}_{C_3}{2}^3{x}^{12-3}.y^3$

$=-{12}_{C_3}.8x^9{y}^3$

$=-220\times 8x^9{y}^3=-1760x^9{y}^3$