Sum these coefficients

Algebra Level 2

Determine the sum of all coefficients of the polynomial

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

Details and assumptions

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

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