Simplify 2 cube root of 54x^4-3 cube root of 16x^4

$2 \sqrt[3]{54 x^{4}} - 3 \sqrt[3]{16 x^{4}}$

Step 1

Simplify each term.

Rewrite $54 x^{4}$ as ${(3 x)}^{3} \cdot (2 x)$ .

Factor $27$ out of $54$ .

$2 \sqrt[3]{27 (2) x^{4}} - 3 \sqrt[3]{16 x^{4}}$

Rewrite $27$ as $3^{3}$ .

$2 \sqrt[3]{3^{3} \cdot 2 x^{4}} - 3 \sqrt[3]{16 x^{4}}$

Factor out $x^{3}$ .

$2 \sqrt[3]{3^{3} \cdot 2 (x^{3} x)} - 3 \sqrt[3]{16 x^{4}}$

Move $2$ .

$2 \sqrt[3]{3^{3} x^{3} \cdot 2 x} - 3 \sqrt[3]{16 x^{4}}$

Rewrite $3^{3} x^{3}$ as ${(3 x)}^{3}$ .

$2 \sqrt[3]{{(3 x)}^{3} \cdot 2 x} - 3 \sqrt[3]{16 x^{4}}$

Add parentheses.

$2 \sqrt[3]{{(3 x)}^{3} \cdot (2 x)} - 3 \sqrt[3]{16 x^{4}}$

Pull terms out from under the radical.

$2 (3 x \sqrt[3]{2 x}) - 3 \sqrt[3]{16 x^{4}}$

Multiply $3$ by $2$ .

$6 (x \sqrt[3]{2 x}) - 3 \sqrt[3]{16 x^{4}}$

Rewrite $16 x^{4}$ as ${(2 x)}^{3} \cdot (2 x)$ .

Factor $8$ out of $16$ .

$6 x \sqrt[3]{2 x} - 3 \sqrt[3]{8 (2) x^{4}}$

Rewrite $8$ as $2^{3}$ .

$6 x \sqrt[3]{2 x} - 3 \sqrt[3]{2^{3} \cdot 2 x^{4}}$

Factor out $x^{3}$ .

$6 x \sqrt[3]{2 x} - 3 \sqrt[3]{2^{3} \cdot 2 (x^{3} x)}$

Move $2$ .

$6 x \sqrt[3]{2 x} - 3 \sqrt[3]{2^{3} x^{3} \cdot 2 x}$

Rewrite $2^{3} x^{3}$ as ${(2 x)}^{3}$ .

$6 x \sqrt[3]{2 x} - 3 \sqrt[3]{{(2 x)}^{3} \cdot 2 x}$

Add parentheses.

$6 x \sqrt[3]{2 x} - 3 \sqrt[3]{{(2 x)}^{3} \cdot (2 x)}$

Pull terms out from under the radical.

$6 x \sqrt[3]{2 x} - 3 (2 x \sqrt[3]{2 x})$

Multiply $2$ by $- 3$ .

$6 x \sqrt[3]{2 x} - 6 x \sqrt[3]{2 x}$

Step 2

Subtract $6 x \sqrt[3]{2 x}$ from $6 x \sqrt[3]{2 x}$ .

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