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\left(4m^{2}n^{3}-5y\right)\left(4m^{2}n^{3}+5y\right)
Rewrite 16m^{4}n^{6}-25y^{2} as \left(4m^{2}n^{3}\right)^{2}-\left(5y\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(-5y+4m^{2}n^{3}\right)\left(5y+4m^{2}n^{3}\right)
Reorder the terms.