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\left(6m^{2}-7n\right)\left(6m^{2}+7n\right)
Rewrite 36m^{4}-49n^{2} as \left(6m^{2}\right)^{2}-\left(7n\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).