(3m+5n)(9m²-15mn+25n²)
1) Let's factorize 27m³ +125n³.
27m³ +125n³ Let's use x³ +y³ product to factorize that
x³ +y³ = (x +y)(x²-xy +y²)
2) So let's rewrite it, since 3³ = 27 and 5³ = 125
27m³ +125n³ =
Plug x =3m and y = 5n into those factors (x +y)(x²-xy +y²)
27m³ +125n³= (3m + 5n)(3²m² -5n*3m +5²n²)
27m³ +125n³= (3m+5n)(9m² - 15mn +25n²)
3) So the answer is
(3m+5n)(9m²-15mn+25n²)