Question

factor $3v^{3}t - 81t$ completely.

Explanation:

Step1: Factor out GCF

$3v^3t - 81t = 3t(v^3 - 27)$

Step2: Recognize difference of cubes

$v^3 - 27 = v^3 - 3^3$

Step3: Apply difference of cubes formula

$v^3 - 3^3 = (v - 3)(v^2 + 3v + 9)$

Step4: Combine all factors

$3t(v - 3)(v^2 + 3v + 9)$

Answer:

$3t(v - 3)(v^2 + 3v + 9)$