Answer
$(x^2+4y^2)(x+2y)(x-2y)$
Work Step by Step
$x^4-16y^4=(x^2)^2-(4y^2)^2=(x^2+4y^2)(x^2-4y^2)=(x^2+4y^2)[(x^2-(2y)^2]=(x^2+4y^2)(x+2y)(x-2y)$
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