Question

Coefficient of $x^{10}$ in the expansion of ${(1+x^2-x^3)}^8$ is

• A. $476$
• B. $496$
• C. $506$
• D. $528$

Answer 1

The correct option is A $476$

$x^{10}$ can be achieved in $2$ ways
$(-x^3{)}^2(x^2{)}^2{1}^4$
The coefficient being
$\frac{8!}{2!.2!4!}=420$
And $(-x^3{)}^0(x^2{)}^5{1}^3$
$\frac{8!}{5!.3!}=56$
Hence the coefficient of $x^{10}$ will be
$420+56$
$=476$