Correct answer: 0
\((1-x)(1-x)^{2007}\left(1+x+x^{2}\right)^{2007}\)
\((1-x)\left(1-x^{3}\right)^{2007}\)
\((1-\mathrm{x})\left({ }^{2007} \mathrm{C}_{0}-{ }^{2007} \mathrm{C}_{1}\left(\mathrm{x}^{3}\right)+\ldots \ldots.\right)\)
General term
\((1-x)\left((-1)^{\mathrm{r}}{ \ }^{2007} \mathrm{C}_{\mathrm{r}}{ }^{3 \mathrm{r}}\right)\)
\((-1)^\mathrm{r} \ ^{2007} \mathrm{C}_{\mathrm{r}} \mathrm{x}^{3 \mathrm{r}}-(-1)^{\mathrm{r}}\ ^{ 2007} \mathrm{C}_{\mathrm{r}} \mathrm{x}^{3 \mathrm{r}+1}\)
\(3 r=2012\)
\(r \neq \frac{2012}{3}\)
\(3 r+1=2012\)
\(3 r=2011\)
\(r \neq \frac{2011}{3}\)
Hence there is no term containing \(\mathrm{x}^{2012}\).
So coefficient of \(\mathrm{x}^{2012}=0\).
