Answer:
[tex]\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)[/tex]
Step-by-step explanation:
[tex]27m^3+125n^3=\left(3m\right)^3+\left(5n\right)^3[/tex]
Apply sum of cubes formula: [tex]x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)[/tex]
[tex]\left(3m\right)^3+\left(5n\right)^3=\left(3m+5n\right)\left(3^2m^2-3m\times 5n+5^2n^2\right)[/tex]
[tex]\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)[/tex]
