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Find the coefficient of t^(8) in the exp...

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

A

`1680`

B

`2140`

C

`2520`

D

`2730`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `((1+2t^(2))-t^(3))^(9)`
`="^(9)C_(0)(1+2t^(2))^(9)-^(9)C_(1)(1+2t^(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 the expansion of `(1+2t^(2)-t^(3))^(9)`
`=^(9)C_(0)("coefficient of" t^(8) "in" (1+2t^(2))^(9)) -^(9)C_(1)("coefficient of" t^(5) "in" (1+2t^(2))^(8))+^(9)C_(2)("coefficient of"t^(2) "in" (1+2t^(2))^(7))`
`=^(9)C_(9)*^(9)C_(4)2^(4)-0+^(9)C_(2)*^(7)C_(1)*2`
`=2520`
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