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\left(2x^{4}+5y\right)\left(4x^{8}+25y^{2}-10yx^{4}\right)
Rewrite 8x^{12}+125y^{3} as \left(2x^{4}\right)^{3}+\left(5y\right)^{3}. The sum of cubes can be factored using the rule: a^{3}+b^{3}=\left(a+b\right)\left(a^{2}-ab+b^{2}\right).