The sum of the coefficients of all the terms in the expansion of $(5 x-9)^{4}$ is __________.

To find the sum of coefficients in any polynomial expansion, substitute $x = 1$.

$=(5x - 9)^4$

$=(5(1) - 9)^4$

$=(5 - 9)^4$

$=(-4)^4$

$=\boxed{256}$

---

How does this work?

When we expand $(5x - 9)^4$, we get: $ax^4 + bx^3 + cx^2 + dx + e$

To find $a + b + c + d + e$, substitute $x = 1$:

$a(1)^4 + b(1)^3 + c(1)^2 + d(1) + e = a + b + c + d + e$

This method works for any polynomial and is much faster than full expansion.

$\therefore$ The sum of coefficients $= 256$

---

You do not have to expand it entirely: