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

$(3-x)\sqrt[3]{2x}$
Simplifying each term and then combining like terms, the given expression, $\sqrt[3]{54x}-\sqrt[3]{2x^4} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt[3]{27\cdot2x}-\sqrt[3]{x^3\cdot2x} \\\\= \sqrt[3]{(3)^3\cdot2x}-\sqrt[3]{(x)^3\cdot2x} \\\\= 3\sqrt[3]{2x}-x\sqrt[3]{2x} \\\\= (3-x)\sqrt[3]{2x} .\end{array} * Note that it is assumed that all variables represent positive numbers.