Question

factor completely. 72u³v - 2uv³

Explanation:

Step1: Factor out GCF

Identify and factor the greatest common factor (GCF) of the two terms. The GCF of $72u^3v$ and $2uv^3$ is $2uv$.
$72u^3v - 2uv^3 = 2uv(36u^2 - v^2)$

Step2: Recognize difference of squares

Notice that $36u^2 - v^2$ is a difference of squares, where $36u^2=(6u)^2$ and $v^2=(v)^2$. Use the difference of squares formula $a^2 - b^2=(a-b)(a+b)$.
$36u^2 - v^2=(6u - v)(6u + v)$

Step3: Combine factors

Substitute the factored form of the difference of squares back into the expression from Step1.
$2uv(36u^2 - v^2)=2uv(6u - v)(6u + v)$

Answer:

$2uv(6u - v)(6u + v)$