Multiply (3+ cube root of 5)(9-3 cube root of 5+ cube root of 25)

$(3 + \sqrt[3]{5}) (9 - 3 \sqrt[3]{5} + \sqrt[3]{25})$

Expand $(3 + \sqrt[3]{5}) (9 - 3 \sqrt[3]{5} + \sqrt[3]{25})$ by multiplying each term in the first expression by each term in the second expression.

$3 \cdot 9 + 3 (- 3 \sqrt[3]{5}) + 3 \sqrt[3]{25} + \sqrt[3]{5} \cdot 9 + \sqrt[3]{5} (- 3 \sqrt[3]{5}) + \sqrt[3]{5} \sqrt[3]{25}$

Simplify terms.

Tap for more steps…

Simplify each term.

Tap for more steps…

Multiply $3$ by $9$ .

$27 + 3 (- 3 \sqrt[3]{5}) + 3 \sqrt[3]{25} + \sqrt[3]{5} \cdot 9 + \sqrt[3]{5} (- 3 \sqrt[3]{5}) + \sqrt[3]{5} \sqrt[3]{25}$

Multiply $- 3$ by $3$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + \sqrt[3]{5} \cdot 9 + \sqrt[3]{5} (- 3 \sqrt[3]{5}) + \sqrt[3]{5} \sqrt[3]{25}$

Move $9$ to the left of $\sqrt[3]{5}$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \cdot \sqrt[3]{5} + \sqrt[3]{5} (- 3 \sqrt[3]{5}) + \sqrt[3]{5} \sqrt[3]{25}$

Multiply $\sqrt[3]{5} (- 3 \sqrt[3]{5})$ .

Tap for more steps…

Raise $\sqrt[3]{5}$ to the power of $1$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 ({\sqrt[3]{5}}^{1} \sqrt[3]{5}) + \sqrt[3]{5} \sqrt[3]{25}$

Raise $\sqrt[3]{5}$ to the power of $1$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 ({\sqrt[3]{5}}^{1} {\sqrt[3]{5}}^{1}) + \sqrt[3]{5} \sqrt[3]{25}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 {\sqrt[3]{5}}^{1 + 1} + \sqrt[3]{5} \sqrt[3]{25}$

Add $1$ and $1$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 {\sqrt[3]{5}}^{2} + \sqrt[3]{5} \sqrt[3]{25}$

Rewrite ${\sqrt[3]{5}}^{2}$ as ${(5^{2})}^{\frac{1}{3}}$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{5^{2}} + \sqrt[3]{5} \sqrt[3]{25}$

Raise $5$ to the power of $2$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{25} + \sqrt[3]{5} \sqrt[3]{25}$

Combine using the product rule for radicals.

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{25} + \sqrt[3]{5 \cdot 25}$

Multiply $5$ by $25$ .

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{25} + \sqrt[3]{125}$

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

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{25} + \sqrt[3]{5^{3}}$

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

$27 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{25} + 5$

Simplify by adding terms.

Tap for more steps…

Add $27$ and $5$ .

$32 - 9 \sqrt[3]{5} + 3 \sqrt[3]{25} + 9 \sqrt[3]{5} - 3 \sqrt[3]{25}$

Add $- 9 \sqrt[3]{5}$ and $9 \sqrt[3]{5}$ .

$32 + 0 + 3 \sqrt[3]{25} - 3 \sqrt[3]{25}$

Add $32$ and $0$ .

$32 + 3 \sqrt[3]{25} - 3 \sqrt[3]{25}$

Subtract $3 \sqrt[3]{25}$ from $3 \sqrt[3]{25}$ .

$32 + 0$

Add $32$ and $0$ .

$32$

Multiply (3+ cube root of 5)(9-3 cube root of 5+ cube root of 25)

Need help with MATH HOMEWORK