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\left(3y-5\right)\left(9y^{2}+15y+25\right)
Rewrite 27y^{3}-125 as \left(3y\right)^{3}-5^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right). Polynomial 9y^{2}+15y+25 is not factored since it does not have any rational roots.