The coefficient of x10 in the expansion of 1+x2−x38 is

we rewrite the given expression as [1 + x2 (1 - x)]8 and expand by using the binomial theorem. We have,1+x2(1−x)8=8C0+8C1x2(1−x)+8C2x4(1−x)2+8C3x6(1−x)3+8C4x8(1−x)4+8C5x10(1−x)5+⋯The two terms which contain x10 are  8C4x8(1−x)4 and  8C5x10(1−x)5.Thus, the coefficient of x10 in the given expression is given by  8C4 [coefficient of x2 in the expansion of (1−x)4] +8C5=8C4(6)+8C5=8!4!4!(6)+8!3!5!=(70)(6)+56=476