## Intermediate Algebra: Connecting Concepts through Application

(2m+5n)(4m$^2$-10mn+25n$^2$)
8m$^3$+125n$^3$ This expression is a sum of cubes. If the cube root of the first term is a and the cube root of the second term is b, then the factorization is (a+b)(a$^2$-ab+b$^2$). So since $\sqrt[3] {8m^3}$=2m $\sqrt[3] {125n^3}$=5n, (2m+5n)(4m$^2$-10mn+25n$^2$).