(1−x)(1−x)2007(1+x+x2)2007 (1−x)(1−x3)2007 (1−x)(2007C0−2007C1(x3)+......) General term (1−x)((−1)r2007Crx3r) (−1)r2007Crx3r−(−1)r2007Crx3r+1 3r=2012 r≠
2012
3
3r+1=2012 3r=2011 r≠
2011
3
Hence there is no term containing x2012. So coefficient of x2012=0