## Intermediate Algebra: Connecting Concepts through Application

(a-5b)(a$^2$+5ab+25b$^2$)
a$^3$-125b$^3$ This expression is a difference 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 $\sqrt[3] {a^3}$=a $\sqrt[3] {125b^3}$=5b (a-5b)(a$^2$+5ab+25b$^2$).