# Write the general term in the expansion of $(x^2-yx)^{12}$

$\begin{array}{1 1}(A)\;x^{24-2r}y^r\\(B)\;\large\frac{(-1)^r12!}{r!(12-r)!}\normalsize x^{24-2r}y^r\\(C)\;\large\frac{(-1)^r12!}{r!(12-r)!}\\(D)\;\text{None of these}\end{array}$

Toolbox:
• $T_{r+1}$=General term =$nC_ra^{n-r}b^r$
General term $T_{r+1}=12C_r(x^2)^{12-r}.(-yx)^r$
$\Rightarrow \large\frac{12!}{r!(12-r)!}$$x^{24-2r}(-1)^ry^rx^r \Rightarrow \large\frac{-1)^r 12!}{r!(12-r)!}$$x^{24-2r}y^r$
Hence (B) is the correct answer.
answered Jun 23, 2014