Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$9 - \sqrt[3]{4 k} \sqrt[3]{2 k} - \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$

Step 1.2

Multiply $- \sqrt[3]{4 k} \sqrt[3]{2 k}$ .

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Step 1.2.1

Combine using the product rule for radicals.

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

Step 1.2.2

Multiply $4$ by $2$ .

$9 - \sqrt[3]{8 k \cdot k} - \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$

Step 1.2.3

Raise $k$ to the power of $1$ .

$9 - \sqrt[3]{8 (k^{1} k)} - \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$

Step 1.2.4

Raise $k$ to the power of $1$ .

$9 - \sqrt[3]{8 (k^{1} k^{1})} - \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$

Step 1.2.5

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

$9 - \sqrt[3]{8 k^{1 + 1}} - \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$

Step 1.2.6

Add $1$ and $1$ .

$9 - \sqrt[3]{8 k^{2}} - \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$

Step 1.3

Multiply $- \sqrt[3]{4 k} \sqrt[3]{2 k^{2}}$ .

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Step 1.3.1

Combine using the product rule for radicals.

$9 - \sqrt[3]{8 k^{2}} - \sqrt[3]{2 k^{2} (4 k)}$

Step 1.3.2

Multiply $4$ by $2$ .

$9 - \sqrt[3]{8 k^{2}} - \sqrt[3]{8 k^{2} k}$

Step 1.3.3

Raise $k$ to the power of $1$ .

$9 - \sqrt[3]{8 k^{2}} - \sqrt[3]{8 (k^{1} k^{2})}$

Step 1.3.4

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

$9 - \sqrt[3]{8 k^{2}} - \sqrt[3]{8 k^{1 + 2}}$

Step 1.3.5

Add $1$ and $2$ .

$9 - \sqrt[3]{8 k^{2}} - \sqrt[3]{8 k^{3}}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$9 - \sqrt[3]{2^{3} k^{2}} - \sqrt[3]{8 k^{3}}$

Step 1.4.2

Pull terms out from under the radical.

$9 - (2 \sqrt[3]{k^{2}}) - \sqrt[3]{8 k^{3}}$

Step 1.4.3

Multiply $2$ by $- 1$ .

$9 - 2 \sqrt[3]{k^{2}} - \sqrt[3]{8 k^{3}}$

Step 1.4.4

Rewrite $8 k^{3}$ as ${(2 k)}^{3}$ .

$9 - 2 \sqrt[3]{k^{2}} - \sqrt[3]{{(2 k)}^{3}}$

Step 1.4.5

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

$9 - 2 \sqrt[3]{k^{2}} - (2 k)$

Step 1.4.6

Multiply $2$ by $- 1$ .

$9 - 2 \sqrt[3]{k^{2}} - 2 k$

Step 2

Simplify the expression.

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Step 2.1

Move $- 2 \sqrt[3]{k^{2}}$ .

$9 - 2 k - 2 \sqrt[3]{k^{2}}$

Step 2.2

Reorder $9$ and $- 2 k$ .

$- 2 k + 9 - 2 \sqrt[3]{k^{2}}$