Question

factor $27 - 125m^3$ completely.

Explanation:

Step1: Identify difference of cubes

$27 = 3^3$, $125m^3=(5m)^3$, so $27-125m^3=3^3-(5m)^3$

Step2: Apply difference of cubes formula

Use $a^3-b^3=(a-b)(a^2+ab+b^2)$, where $a=3$, $b=5m$

Step3: Substitute values into formula

$(3 - 5m)(3^2 + 3\cdot5m + (5m)^2)$

Step4: Simplify the second factor

$(3 - 5m)(9 + 15m + 25m^2)$

Answer:

$(3 - 5m)(9 + 15m + 25m^2)$