Answer
$(3a-v)^2$
Work Step by Step
RECALL:
$A^2-2AB+B^2=(A-B)^2$
The given trinomial can be written as:
$=(3a)^2-2(3a)(v) + v^2$
The expression above is a perfect square trinomial with $A=3a$ and $B=v$
Factor using the formula above to obtain:
$=(3a-v)^2$