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Find the coefficient of x^(12) in expans...

Find the coefficient of `x^(12)` in expansion of `(1-x^(2)+x^(4))^(3)(1-x)^(7)`.

Text Solution

Verified by Experts

The correct Answer is:
99
`((1-x^(2))+x^(4))^(3)(1-x)^(7)`
`= ((1-x^(2))^(3)+3x^(4)(1-x^(2))^(3) +3x^(4)(1-x^(2))^(2)+3x^(8)(1-x^(2))+x^(12))xx(.^(7)C_(0) - .^(7)C_(1)x+.^(7)C_(2)x^(2)-"…….."-.^(7)C_(7)x^(7))`
`:.` Coefficient of `x^(12) = .^(7)C_(0) - 3 xx .^(7)C_(2) + 6 xx .^(7)C_(4) - 7 xx .^(7)C_(6)`
` = 99`
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