Chapter 5 - Polynomials and Factoring - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set - Page 338: 31

$5(x-2z)(x^2+2xz+4z^2)$

Factoring the $GCF= 5 ,$ the given expression, $ 5x^3-40z^3 ,$ is equivalent to \begin{array}{l} 5(x^3-8z^3) .\end{array} Using $a^3+b^3=(a+b)(a^2-ab+b^2)$ or the factoring of 2 cubes, the factored form of the expression, $ 5(x^3-8z^3) ,$ is \begin{array}{l} 5(x-2z)[ (x)^2-(x)(-2z)+(-2z)^2] \\\\= 5(x-2z)(x^2+2xz+4z^2) .\end{array}