Question

1. $4sqrt3{32x^3} - sqrt3{108x^3}$

Explanation:

Step1: Simplify cube roots

First, factor the radicands to extract perfect cubes:
$4\sqrt[3]{32x^3} = 4\sqrt[3]{8x^3 \cdot 4} = 4 \cdot 2x\sqrt[3]{4} = 8x\sqrt[3]{4}$
$\sqrt[3]{108x^3} = \sqrt[3]{27x^3 \cdot 4} = 3x\sqrt[3]{4}$

Step2: Subtract like terms

Subtract the simplified terms:
$8x\sqrt[3]{4} - 3x\sqrt[3]{4}$

Answer:

$5x\sqrt[3]{4}$