In the expansion of ( 1 + 3 x + 2 x 2 ) 6 , the coefficient of x 11 is

Question

In the expansion of ${(1 + 3 x + 2 x^{2})}^{6}$ , the coefficient of $x^{11}$ is

Smart Achievers · Accepted Answer

(4)

$We have, {(1 + 3 x + 2 x^{2})}^{6} = ((1 + 3 x) + {(2 x^{2}))}^{6}$

$= {}^{6}C_{0} {(1 + 3 x)}^{6} + {}^{6}C_{1} {(1 + 3 x)}^{5} 2 x^{2} + {}^{6}C_{2} {(1 + 3 x)}^{4} {(2 x^{2})}^{2}$ $+ {}^{6}C_{3} {(1 + 3 x)}^{3} {(2 x^{2})}^{3} + {}^{6}C_{4} {(1 + 3 x)}^{2} {(2 x^{2})}^{4}$ $+ {}^{6}C_{5} (1 + 3 x) {(2 x^{2})}^{5} + {}^{6}C_{6} {(2 x^{2})}^{6}$

Coefficient of $x^{11}$ in above expression is

${}^{6}C_{5} \cdot 3 \cdot 32 = 6 \times 3 \times 32 = 576$

Solution

Q.
In the expansion of ${(1 + 3 x + 2 x^{2})}^{6}$ , the coefficient of $x^{11}$ is

1 144

2 288

3 216

4 576

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