Find the coefficient of `x^(15)` in the expansion of `(x - x^(2))^(10)`

Explanation

Given expansion is `(x - x^(2))_(10)`
Let the term `T_(r + 1)` is the general term
`:. T_(r + 1) = .^(10)C_(r) x^(10 - r) (-x^(2))^(r)`
`= (-1)^(r) . .^(10)C_(r). X^(10 - r) . X^(2r)`
`= (-1)^(r) .^(10)C_(r) x^(10 + r)`
For the coefficient of `x^(15)`,
`10 + r = 15 rArr r = 5`
`T_(5 + 1) = (-1)^(5) .^(10)C_(5) x^(15)`
`:.` Coefficient of `x^(15) = - (10 xx 9 xx 8 xx 7 xx 6 xx 5!)/(5 xx 4 xx 3 xx 2 xx 1 xx 5!)`
`= - 3 xx 2 xx 7 xx 6 = -252`