Determine the coefficient of x^15 in the expansion (2x-3x^2)^10

Question

ii)Find the coefficient of x^-8 in the expansion (x^2 +1/x^3)^16

Answer 1

General term:
term(n+1) = C(10,n) (2x)^n (-3x^2)^(10-n)
= C(10,n) (2^n) x^n (-3)^(10-n) (x^2)^(10-n)
= C(10,n) 2^n (-3)^(10-n) x^(20-n)
we want x^(20-n) = x^15
20-n = 15
n = 5
So the coefficient is C(10,5)(2^5)(-3)^5
= 252(32)(-243) = 1,959,552
check my arithmetic

do the 2nd part the same way.

Answer 2

I think it's supposed to be -1959552

Answer 3

Sorry but the part where u said (x^2)^{10-n)=x^20 -n

Answer 4

You should have been 100% sure that it was -1959552 looking at
my 252(32)(-243)

regarding you second concern:
notice that there were 2 factors containing the base x

(x^n)(x^2)^(10-n)
= (x^n)(x^(20 - 2n) )
= x^(n + 20 - 2n)
= x^(20-n)