Here we can find the sum of the coefficients of the odd powers of x in given expansion. We have (1+x+x2)5 We know that To find the sum of coefficients of odd powers of x, we find the values of the expression by replacing the variables by 1 and -1 respectively and then subtracting the two results. Let f(x) = (1+x+x2)5 Replacing the variables by 1 and -1 f(1) = (1+1+1)5 = 35 f(-1) = (1+(−1)+1)5 = (1)5 = 1 By subtracting the two results we get the odd powers of x.
f(1)−f(−1)
2
=
35−1
2
=
243−1
2
=
242
2
= 121 Hence, The sum of the coefficients of the odd powers of x in the expansion of (1+x+x2)5 is