Question

X^10 then (x^2 -1/x^3)^10=??

Answer 1

Answer:

1

$( \frac{ {x}^{2} - 1}{ {x}^{3} } ) { }^{10} \\ \\ = (x - {x}^{ - 3} ) {}^{10} \\ \\ = {x}^{10} (1 - {x}^{ - 4} ) {}^{10}$

So coefficient will be equal to constant term in

$(1 - {x}^{ - 4} ) {}^{10} \\ \\ = \sum _{r = 0} ^{10} \binom{10}{r}( - {x}^{ - 4} ) {}^{r}$

Constant term when r = 0

So

Coefficient will be

$\binom{10}{0} = 1$