Simplify 2 cube root of 54x^4-x cube root of 250x

$2 \sqrt[3]{54 x^{4}} - x \sqrt[3]{250 x}$

Step 1

Simplify each term.

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

Factor $27$ out of $54$ .

$2 \sqrt[3]{27 (2) x^{4}} - x \sqrt[3]{250 x}$

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

$2 \sqrt[3]{3^{3} \cdot 2 x^{4}} - x \sqrt[3]{250 x}$

Factor out $x^{3}$ .

$2 \sqrt[3]{3^{3} \cdot 2 (x^{3} x)} - x \sqrt[3]{250 x}$

Move $2$ .

$2 \sqrt[3]{3^{3} x^{3} \cdot 2 x} - x \sqrt[3]{250 x}$

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

$2 \sqrt[3]{{(3 x)}^{3} \cdot 2 x} - x \sqrt[3]{250 x}$

Add parentheses.

$2 \sqrt[3]{{(3 x)}^{3} \cdot (2 x)} - x \sqrt[3]{250 x}$

Pull terms out from under the radical.

$2 (3 x \sqrt[3]{2 x}) - x \sqrt[3]{250 x}$

Multiply $3$ by $2$ .

$6 (x \sqrt[3]{2 x}) - x \sqrt[3]{250 x}$

Rewrite $250 x$ as $5^{3} \cdot (2 x)$ .

Factor $125$ out of $250$ .

$6 x \sqrt[3]{2 x} - x \sqrt[3]{125 (2) x}$

Rewrite $125$ as $5^{3}$ .

$6 x \sqrt[3]{2 x} - x \sqrt[3]{5^{3} \cdot 2 x}$

Add parentheses.

$6 x \sqrt[3]{2 x} - x \sqrt[3]{5^{3} \cdot (2 x)}$

Pull terms out from under the radical.

$6 x \sqrt[3]{2 x} - x (5 \sqrt[3]{2 x})$

Multiply $5$ by $- 1$ .

$6 x \sqrt[3]{2 x} - 5 x \sqrt[3]{2 x}$

Step 2

Simplify by adding terms.

Subtract $5 x \sqrt[3]{2 x}$ from $6 x \sqrt[3]{2 x}$ .

$1 x \sqrt[3]{2 x}$

Multiply $x$ by $1$ .

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