Question

Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x¹⁰?

Answer 1

Let T_r+1 contain x¹⁰.

Then T_r+1 = `""^18"C"_r  (x^2)^(18 - r)  (-2^r)/x`

= `""^18"C"_r  x^(36 - 2r)  (-1)^r  * 2^r  x^(-r)`

= `(-1)^r  2^r  ""^18"C"_r  x^(36 - 3r)`

Thus, 36 – 3r = 10

i.e., r = `36/3`

Since r is a fraction, the given expansion cannot have a term containing x¹⁰.