Find the coefficient of `x^8` in the expansion of`(x^2-1/x)^(10)`

Explanation

Here , ` T_(r +1) = ""^(10)C_(r) (x^(2))^(10-r) (-(1)/(x))^(r)`
` = ""^(10)C_(r) x^(20 - 2r) .(-1)^(r) . (1)/(x^(r)) `
` = ""^(10)C_(r) (-1)^(r) . x^(20 - 3r)` …(i)
Now , in order to find out the coefficient of `x^(6) , 20 - 3r ` must be 8.
i.e. ` 20 - 3r = 8`
` therefore r = 4 `
Hence , puttingh r = 4 in Eq . (i) we get
Required coefficient ` = (-1)^(4) . ""^(10)C_(4) = (10*9*8*7)/(1*2*3*4) = 210 ` .