Answer
$xy(x+4y)(x-4y)$
Work Step by Step
The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$.
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: $x^3y-16xy^3=\\=xy(x^2-16y^2)\\=xy(x^2-(4y)^2)\\=xy(x+4y)(x-4y)$
