The problem asks to factor the expression $1-125x^3$ using the difference of cubes formula.

1. Problem Description

The problem asks to factor the expression $1-125x^3$ using the difference of cubes formula.

2. Solution Steps

The expression is in the form of $a^3 - b^3$, where $a^3 = 1$ and $b^3 = 125x^3$.

Therefore, $a = \sqrt[3]{1} = 1$ and $b = \sqrt[3]{125x^3} = 5x$.

The difference of cubes formula is:

$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$.

Substituting $a=1$ and $b=5x$ into the formula, we have:

$1^3 - (5x)^3 = (1 - 5x)(1^2 + 1(5x) + (5x)^2)$

$1 - 125x^3 = (1 - 5x)(1 + 5x + 25x^2)$.

3. Final Answer

$(1-5x)(1+5x+25x^2)$