Determine the constant term in the expansion of

Question

(X-(2/x^2))^9

Answer 1

The binomial theorem gives the terms as (9Ck)•x^k•(-2/x²)^9-k for k=0,1,...,9. We can rewrite this as (9Ck)(-2)^9-k•x^3k-18. The constant term is the same as the coefficient on the zero-degree term, which occurs when k=6. The coefficient on it is (9C6)(-2)³ = -672.

Answer 2

( X -2/x^2)^9

first of all find inside of parenthesis

(x^3 - 2 )/ x^2

now this fraction to the power 9

(x^3 - 2 )^9 / x^18

For finding constant term in the expansion of is (-2)^9 = -512

I hope it is useful,

Minoo