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In the expansion of (1+3x+2x^2)^6 , the ...

In the expansion of `(1+3x+2x^2)^6` , the coefficient of `x^(11)` is a. 144 b. 288 c. 216 d. 576

Text Solution

Verified by Experts

The correct Answer is:
576
`(1+3x+2x^(3))^(6) = [1+x(3+2x)]^(6)`
`= 1+.^(6)C_(1)x(3+2x) + .^(6)C_(2)x^(2)(3+2x)^(2) + .^(6)C_(3)x^(3)(3+2x)^(3) +.^(6)C_(4)x^(4)(3+2x)^(4) + .^(6)C_(5)x^(5)(3+2x)^(5) + .^(6)C_(6)x^(6)(3+2x)^(6)`
We get `x^(11)` only from `.^(6)C_(6)x^(6)(3+2x)^(6)`
`:.` Coefficient of `x^(11) = .^(6)C_(5)xx3xx2^(5) = 576`
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