Algebra Examples

$\sqrt[3]{y^{2}} (5 \sqrt[3]{8 y} + \sqrt[3]{y} - 9 \sqrt[3]{y^{4}})$

Step 1

Simplify each term.

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Step 1.1

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

$\sqrt[3]{y^{2}} (5 \sqrt[3]{2^{3} y} + \sqrt[3]{y} - 9 \sqrt[3]{y^{4}})$

Step 1.2

Pull terms out from under the radical.

$\sqrt[3]{y^{2}} (5 (2 \sqrt[3]{y}) + \sqrt[3]{y} - 9 \sqrt[3]{y^{4}})$

Step 1.3

Multiply $2$ by $5$ .

$\sqrt[3]{y^{2}} (10 \sqrt[3]{y} + \sqrt[3]{y} - 9 \sqrt[3]{y^{4}})$

Step 1.4

Factor out $y^{3}$ .

$\sqrt[3]{y^{2}} (10 \sqrt[3]{y} + \sqrt[3]{y} - 9 \sqrt[3]{y^{3} y})$

Step 1.5

Pull terms out from under the radical.

$\sqrt[3]{y^{2}} (10 \sqrt[3]{y} + \sqrt[3]{y} - 9 y \sqrt[3]{y})$

Step 2

Simplify terms.

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Step 2.1

Add $10 \sqrt[3]{y}$ and $\sqrt[3]{y}$ .

$\sqrt[3]{y^{2}} (11 \sqrt[3]{y} - 9 y \sqrt[3]{y})$

Step 2.2

Apply the distributive property.

$\sqrt[3]{y^{2}} (11 \sqrt[3]{y}) + \sqrt[3]{y^{2}} (- 9 y \sqrt[3]{y})$

Step 2.3

Reorder.

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Step 2.3.1

Rewrite using the commutative property of multiplication.

$11 \sqrt[3]{y^{2}} \sqrt[3]{y} + \sqrt[3]{y^{2}} (- 9 y \sqrt[3]{y})$

Step 2.3.2

Rewrite using the commutative property of multiplication.

$11 \sqrt[3]{y^{2}} \sqrt[3]{y} - 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$

Step 3

Simplify each term.

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Step 3.1

Multiply $11 \sqrt[3]{y^{2}} \sqrt[3]{y}$ .

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Step 3.1.1

Combine using the product rule for radicals.

$11 \sqrt[3]{y \cdot y^{2}} - 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$

Step 3.1.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 3.1.2.1

Multiply $y$ by $y^{2}$ .

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Step 3.1.2.1.1

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

$11 \sqrt[3]{y^{1} y^{2}} - 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$

Step 3.1.2.1.2

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

$11 \sqrt[3]{y^{1 + 2}} - 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$

Step 3.1.2.2

Add $1$ and $2$ .

$11 \sqrt[3]{y^{3}} - 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$

Step 3.2

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

$11 y - 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$

Step 3.3

Multiply $- 9 \sqrt[3]{y^{2}} (y \sqrt[3]{y})$ .

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Step 3.3.1

Combine using the product rule for radicals.

$11 y - 9 (y \sqrt[3]{y^{2} y})$

Step 3.3.2

Multiply $y^{2}$ by $y$ by adding the exponents.

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Step 3.3.2.1

Multiply $y^{2}$ by $y$ .

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Step 3.3.2.1.1

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

$11 y - 9 (y \sqrt[3]{y^{2} y^{1}})$

Step 3.3.2.1.2

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

$11 y - 9 (y \sqrt[3]{y^{2 + 1}})$

Step 3.3.2.2

Add $2$ and $1$ .

$11 y - 9 (y \sqrt[3]{y^{3}})$

Step 3.4

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

$11 y - 9 (y \cdot y)$

Step 3.5

Multiply $y$ by $y$ .

$11 y - 9 y^{2}$