What is the coefficient of $x^3$ in expansion of $(x^2 - x + 2)^{10}$ 
What is the coefficient of $x^3$ in expansion of $(x^2 - x + 2)^{10}$.

I have tried:  
$$\frac{10!}{(3!\times7!)} \times (-x + 2)^7 \times (x^2)^3  $$
But got an incorrect answer $-15360$.

For a problem of this size, I would just ploddingly take a few derivatives:
$$\begin{align}
f(x)=(x^2-x+2)^{10}
&\implies f'(x)=10(x^2-x+2)^9(2x-1)\\
&\implies f''(x)=90(x^2-x+2)^8(2x-1)^2+20(x^2-x+2)^9\\
&\implies f'''(x)=720(x^2-x+2)^7(2x-1)^3+360(x^2-x+2)^8(2x-1)+180(x^2-x+2)^8(2x-1)\\
&\implies f'''(0)=-720\cdot2^7-360\cdot2^8-180\cdot2^8=-(720+1080)2^7=-1800\cdot128\\
\end{align}$$
The coefficient of $x^3$ is $f'''(0)/6=-300\cdot128=-38400$.
