Simplify cube root of 9(2 cube root of 3+3 cube root of 3-4 cube root of 3)

$\sqrt[3]{9} (2 \sqrt[3]{3} + 3 \sqrt[3]{3} - 4 \sqrt[3]{3})$

Step 1

Add $2 \sqrt[3]{3}$ and $3 \sqrt[3]{3}$ .

$\sqrt[3]{9} (5 \sqrt[3]{3} - 4 \sqrt[3]{3})$

Step 2

Subtract $4 \sqrt[3]{3}$ from $5 \sqrt[3]{3}$ .

$\sqrt[3]{9} \sqrt[3]{3}$

Step 3

Combine using the product rule for radicals.

$\sqrt[3]{9 \cdot 3}$

Step 4

Write the expression using exponents.

Multiply $9$ by $3$ .

$\sqrt[3]{27}$

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

$\sqrt[3]{3^{3}}$

Step 5

Pull terms out from under the radical, assuming real numbers.

$3$