## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(3p+5)(3p-5)^2$
Using factoring by grouping, the factored form of the given expression, $27p^3-45p^2-75p+125 ,$ is \begin{array}{l}\require{cancel} (27p^3-45p^2)-(75p-125) \\\\= 9p^2(3p-5)-25(3p-5) \\\\= (3p-5)(9p^2-25) \end{array} Using $x^2-y^2=(x+y)(x-y)$ or the factoring of the difference of 2 squares, then the factored form of the expression, $(3p-5)(9p^2-25) ,$ is \begin{array}{l} (3p-5)(3p+5)(3p-5) \\\\= (3p+5)(3p-5)(3p-5) \\\\= (3p+5)(3p-5)^2 \end{array}