## Intermediate Algebra: Connecting Concepts through Application

(3m-1)(9m$^2$+3m+1)
27x$^3$-1 This expression is a difference of cubes. If a is the cube root of the first term and b is the cube root of the second term, the factorization is (a-b)(a$^2$+ab+b$^2$. $\sqrt[3] {27m^3}$=3m and $\sqrt[3] 1$=1. So the factorization is (3m-1)(9m$^2$+3m+1).