Chapter 5 - Polynomials and Factoring - 5.5 Factoring Sums or Differences of Cubes - 5.5 Exercise Set - Page 338: 32

$2(y-3z)(y^2+3yz+9z^2)$

Factoring the $GCF= 2 ,$ the given expression, $ 2y^3-54z^3 ,$ is equivalent to \begin{array}{l} 2(y^3-27z^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, $ 2(y^3-27z^3) ,$ is \begin{array}{l} 2(y-3z)[ (y)^2-(y)(-3z)+(-3z)^2] \\\\= 2(y-3z)(y^2+3yz+9z^2) .\end{array}