Answer
$9a^{2n}-6a^nb^n+b^{2n}$
Work Step by Step
The square of a binomial sum is: $(A+B)^2=A^2+2AB+B^2$.
The square of a binomial difference is: $(A-B)^2=A^2-2AB+B^2$.
Hence here: $(3a^n-b^n)^2=(3a^n)^2-2\cdot3a^n\cdot b^n+(b^n)^2=9a^{2n}-6a^nb^n+b^{2n}$