The expression 1 - 125n^3 is factored as a difference of cubes, resulting in the factors (1 - 5n)(1 + 5n + 25n^2) using the identity a^3 - b^3 = (a - b)(a^2 + ab + b^2).
To factor the expression 1 − 125n^3, we can recognize it as a difference of cubes. A difference of cubes can be factored using the identity a^3 − b^3 = (a − b)(a^2 + ab + b^2).
In this case, we can consider 1 as 1^3 and 125n^3 as (5n)^3.
Therefore, the expression can be factored as:
(1 − 5n)(1^2 + (1)(5n) + (5n)^2)
(1 − 5n)(1 + 5n + 25n^2)
These are the correct factors for the expression using polynomial identities.