Sum these coefficients

Algebra Level 2

Determine the sum of all coefficients of the polynomial

f(x)=(3x33x1)38(2x+1)4(x43x2+5x2)77.f(x) = (3x^3-3x-1)^{38}\cdot(2x+1)^4\cdot(x^4-3x^2+5x-2)^{77}.

Details and assumptions

After expanding out the expression for f(x)f(x) given in the problem, one will arrive at a formula that looks like f(x)=anxn+an1xn1++a1x+a0f(x)=a_n x^n+a_{n-1}x^{n-1}+\dotsc+a_1 x+a_0, where a0,a1,a2,,ana_0,a_1,a_2,\dotsc,a_n are numbers. The sum of coefficients of f(x)f(x) is an+an1++a1+a0 a_n + a_{n-1} + \ldots + a_1 + a_0 .


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