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