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\left(4+xy\right)\left(4-xy\right)
Rewrite 16-x^{2}y^{2} as 4^{2}-\left(-xy\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\left(xy+4\right)\left(-xy+4\right)
Reorder the terms.