Simplify cube root of 40x- cube root of 135x

$\sqrt[3]{40 x} - \sqrt[3]{135 x}$

Step 1

Simplify each term.

Rewrite $40 x$ as $2^{3} \cdot (5 x)$ .

Factor $8$ out of $40$ .

$\sqrt[3]{8 (5) x} - \sqrt[3]{135 x}$

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

$\sqrt[3]{2^{3} \cdot 5 x} - \sqrt[3]{135 x}$

Add parentheses.

$\sqrt[3]{2^{3} \cdot (5 x)} - \sqrt[3]{135 x}$

Pull terms out from under the radical.

$2 \sqrt[3]{5 x} - \sqrt[3]{135 x}$

Rewrite $135 x$ as $3^{3} \cdot (5 x)$ .

Factor $27$ out of $135$ .

$2 \sqrt[3]{5 x} - \sqrt[3]{27 (5) x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $3$ by $- 1$ .

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

Step 2

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

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