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Find the coefficient of t^8 in the expa...

Find the coefficient of `t^8` in the expansion of `(1+2t^2-t^3)^9`.

Text Solution

Verified by Experts

The correct Answer is:
2520
`E = (1+2r^(2)-t^(3))^(9)`
`=.^(9)C_(0)(2+2t^(2))^(8) - .^(9)C_(1)(1+2r^(2))^(8).t^(3) + .^(9)C_(2)(1+2t^(2))^(7).t^(6)-.^(9)C_(3)(1+2t^(2))^(6). t^(9) + ......."-.^(9)C_(9)(t^(3))^(9)`
`:.` Coefficient of `t^(8)` in `E = .^(9)C_(0)` (Coefficient of `t^(8)` in `(1+2t^(2))^(9)`)
`-.^(9)C_(1)` (Coefficient of `t^(5)` in `(1+2t^(2))^(9)`)
`+.^(9)C_(2)`(Coefficient of `t^(2)` in `(1+2r^(2))^(7)`)
`= .^(9)C_(0)..^(9)C_(4). 2^(4) - 0 + .^(9)C_(3)^(2) - .^(7)C_(1) . 2`
`= 2520`
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