Question

factor $25cv^{2}-c^{3}$ completely.

Explanation:

Step1: Factor out GCF

Identify and factor out the greatest common factor $c$ from both terms.
$25cv^2 - c^3 = c(25v^2 - c^2)$

Step2: Apply difference of squares

Recognize $25v^2 - c^2$ as a difference of squares, which follows $a^2 - b^2=(a-b)(a+b)$ where $a=5v$, $b=c$.
$25v^2 - c^2 = (5v - c)(5v + c)$

Step3: Combine factors

Substitute the factored form back into the expression from Step1.
$c(25v^2 - c^2) = c(5v - c)(5v + c)$

Answer:

$c(5v - c)(5v + c)$