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Write the general term in the expansion of $\left(x^2-y x\right)^{12}$, $x \neq 0$
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Verified Answer
Binomial expansion is $\left(x^2-y x\right)^{12}$
General term $T_{r+1}={ }^{12} C_r\left(x^2\right)^{12-\mathrm{r}} \cdot(-y x)^{\mathrm{r}}$
$\begin{aligned}
&=\frac{12 !}{r !(12-r) !} \cdot x^{24-2 r} \cdot(-1)^r \cdot y^r x^r \\
&=\frac{(-1)^r 12 !}{r !(12-r) !} \cdot x^{24-r} \cdot y^r
\end{aligned}$
General term $T_{r+1}={ }^{12} C_r\left(x^2\right)^{12-\mathrm{r}} \cdot(-y x)^{\mathrm{r}}$
$\begin{aligned}
&=\frac{12 !}{r !(12-r) !} \cdot x^{24-2 r} \cdot(-1)^r \cdot y^r x^r \\
&=\frac{(-1)^r 12 !}{r !(12-r) !} \cdot x^{24-r} \cdot y^r
\end{aligned}$
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