Out of proportion expansion

The function $f(x)$ can be expanded into a polynomial with integer coefficients $a_n$ as follows:

$\begin{aligned} f(x) & = (1-2x+2x^2)^{743} (2 + 3x - 4x^2 )^{744} \\ & = a_{2974}x^{2974} + a_{2973}x^{2973} + a_{2972}x ^{2972} + ... + a_{2}x^{2} + a_1x + a_0 \end{aligned}$

We note that $f(1)$ gives us the sum of the coefficients.

$\begin{aligned} f(1) & = a_{2974} + a_{2973} + a_{2972} + ... + a_{2} + a_1 + a_0 \\ & = (1-2+2)^{743} (2 + 3 - 4)^{744} \\ & = \boxed{1} \end{aligned}$

Simply substitute x=1 to find the sum of coefficients