Simplify (5 cube root of x+5)( cube root of x+1)

$(5 \sqrt[3]{x} + 5) (\sqrt[3]{x} + 1)$

Step 1

Expand $(5 \sqrt[3]{x} + 5) (\sqrt[3]{x} + 1)$ using the FOIL Method.

Apply the distributive property.

$5 \sqrt[3]{x} (\sqrt[3]{x} + 1) + 5 (\sqrt[3]{x} + 1)$

Apply the distributive property.

$5 \sqrt[3]{x} \sqrt[3]{x} + 5 \sqrt[3]{x} \cdot 1 + 5 (\sqrt[3]{x} + 1)$

Apply the distributive property.

$5 \sqrt[3]{x} \sqrt[3]{x} + 5 \sqrt[3]{x} \cdot 1 + 5 \sqrt[3]{x} + 5 \cdot 1$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $5 \sqrt[3]{x} \sqrt[3]{x}$ .

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

$5 ({\sqrt[3]{x}}^{1} \sqrt[3]{x}) + 5 \sqrt[3]{x} \cdot 1 + 5 \sqrt[3]{x} + 5 \cdot 1$

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

$5 ({\sqrt[3]{x}}^{1} {\sqrt[3]{x}}^{1}) + 5 \sqrt[3]{x} \cdot 1 + 5 \sqrt[3]{x} + 5 \cdot 1$

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

$5 {\sqrt[3]{x}}^{1 + 1} + 5 \sqrt[3]{x} \cdot 1 + 5 \sqrt[3]{x} + 5 \cdot 1$

Add $1$ and $1$ .

$5 {\sqrt[3]{x}}^{2} + 5 \sqrt[3]{x} \cdot 1 + 5 \sqrt[3]{x} + 5 \cdot 1$

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

$5 \sqrt[3]{x^{2}} + 5 \sqrt[3]{x} \cdot 1 + 5 \sqrt[3]{x} + 5 \cdot 1$

Multiply $5$ by $1$ .

$5 \sqrt[3]{x^{2}} + 5 \sqrt[3]{x} + 5 \sqrt[3]{x} + 5 \cdot 1$

Multiply $5$ by $1$ .

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

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

$5 \sqrt[3]{x^{2}} + 10 \sqrt[3]{x} + 5$