The coefficient of x3 in the expansion of (1−x+x2)6 is

(1−x+x2)6=[1−x(1−x)]6 =6C0−6C1x(1−x)+6C2x2(1−x)2−6C3x3(1−x)3+…to 7 terms =6C0−6C1x(1−x)+6C2x2(1−2x+x2)−6C3x3(1−3x+3x2−x3)+…to 7 terms∴Coefficient of x3=−2⋅6C2−6C3 (collecting coefficients of x3 from each term)=−26!2!4!−6!3!3!=−50