Question

factor ( v^2x^2 - 10vx^2 + 25x^2 ) completely.

Explanation:

Step1: Factor out common term

Identify and factor out the greatest common factor $x^2$ from all terms.
$v^2x^2 - 10vx^2 + 25x^2 = x^2(v^2 - 10v + 25)$

Step2: Factor quadratic expression

Recognize $v^2 - 10v + 25$ as a perfect square trinomial, which follows the pattern $a^2-2ab+b^2=(a-b)^2$ where $a=v$, $b=5$.
$v^2 - 10v + 25 = (v - 5)^2$

Step3: Combine the factors

Substitute the factored quadratic back into the expression from Step1.
$x^2(v^2 - 10v + 25) = x^2(v - 5)^2$

Answer:

$x^2(v - 5)^2$