The coefficient of x4 in the expansion of (1 + x + x2 + x3)6 is

A
120
B
160
C
210
D
270

Solution:

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

$= ({}^{6}C_{0} + {}^{6}C_{1} x^{2} + {}^{6}C_{2} x^{4} + \dots + {}^{6}C_{6} x^{12}) ({}^{6}C_{0} + {}^{6}C_{1} x + {}^{6}C_{2} x^{2} + \dots + {}^{6}C_{6} x^{6})$

Coefficient of x⁴ is ${}^{6}C_{0} {}^{6}C_{4} + {}^{6}C_{1} {}^{6}C_{2} + {}^{6}C_{2} {}^{6}C_{0} = 15 + 90 + 15 = 120$ .

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The coefficient of x⁴ in the expansion of (1 + x + x² + x³)⁶ is

Solution:

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