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\left(xy-7z\right)\left(xy+7z\right)
Rewrite x^{2}y^{2}-49z^{2} as \left(xy\right)^{2}-\left(7z\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).