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The coefficient of x^(7) in the expansio...

The coefficient of `x^(7)` in the expansion of `(1-x-x^(3)+x^(4))^(8)` is equal to

A

(a) `-648`

B

(b) `792`

C

(c) `-792`

D

(d) `648`

Text Solution

Verified by Experts

The correct Answer is:
C
`(1-x-x^(2)+x^(4))^(8)=(1-x)^(8)(1-x^(3))^(8)`
`= (1-.^(8)C_(1)x+.^(8)C_(1)x^(2)-.^(8)C_(3)x^(3)+"….")xx(1-.^(8)C_(1)x^(3)+.^(8)C_(2)x^(6)-.^(8)C_(3)x^(9)+"…..")`
`:.` Coefficient of `x^(7)= -.^(8)C_(7)-.^(8)C_(1)xx.^(8)C_(4)-.^(8)C_(1) xx.^(8)C_(2)`
`= - 792`
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