Question

(x⁴-1/x³)¹5 ,
Then find the coefficient of x³² in this question

Answer 1

so $(x^4-\frac{1}{x^3})^{15}$

so through binomial expansion  for (r + 1) term  in $(a+x)^n$  we know  

$T_{r+1}=^nC_ra^{n-r}x^r$

similarly for  $(x^4-\frac{1}{x^3})^{15}$

so let us forget about the coefficient part ($^nC_r$)

so $x^{32}=x^{60-4r}*\frac{1}{x^3r}$

⇒ $x^{32}=x^{60-7r}$

so 32 = 60 - 7r

⇒ 7r = 28 ⇒ r = 4

so the coefficient is =  $^15C_4$ = 1380 ANSWER