Multinomial expansion

Question

$The sum of the coefficients of odd powers of x in the expansion of {(1 + x - x^{2} - x^{3})}^{6} is$

Moderate

A

0
B

32
C

64
D

-1

Solution

Sum of the coefficients of odd powers of x in f(x) is $\frac{f (1) - f (- 1)}{2} = \frac{(1 + 1 - 1 - 1)^{6} - (1 - 1 - 1 + 1)^{6}}{2} = 0$

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