Find the coefficient of `x^4` in the expansion of `(x//2-3//x^2)^(10)dot`

Explanation

In the expansion of `(x//2 - 3//x)^(10)`, the general term is
`T_(r+1) = .^(10)C_(r) (x/2)^(10-r)(-(3)/(x^(2)))^(r)`,
`= .^(10)C_(r) (-1)^(r) '(3^(r))/(2^(10-r))x^(10-3r)`
Here the exponent of x is
`10 - 3r = 4` or `r = 2`
`:. T_(2+1) = .^(10)C_(2)(x/2)^(8)(-(3)/(x^(2)))^(2)`
`= (10 xx 9)/(1xx 2) xx 1/(2^(8)) xx 3^(2) xx x^(4)`
`= (405)/(256)x^(4)`
Therefore, the requ ired coefficient is `405//256`.