Answer
$(3x - 2)\sqrt[3]{2x}$
Work Step by Step
Simplify each radical by factoring the radicand so that at least one factor is a perfect cube to obtain:
$=\sqrt[3]{27x^3(2x)} - \sqrt[3]{8(2x)}
\\=\sqrt[3]{(3x)^3(2x)} - \sqrt[3]{(2^3)(2x)}
\\=3x\sqrt[3]{2x} - 2\sqrt[3]{2x}$
RECALL:
The distributive property states that for any real numbers a, b, and c:
(1) $ac + bc = (a+b)c$
(2) $ac-bc=(a-b)c$
Use the rule (2) above to combine like terms and obtain:
$=(3x - 2)\sqrt[3]{2x}$
