Basic Math Examples

$(\sqrt[3]{y} + 6) (\sqrt[3]{y} - 7)$

Step 1

Expand $(\sqrt[3]{y} + 6) (\sqrt[3]{y} - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt[3]{y} (\sqrt[3]{y} - 7) + 6 (\sqrt[3]{y} - 7)$

Step 1.2

Apply the distributive property.

$\sqrt[3]{y} \sqrt[3]{y} + \sqrt[3]{y} \cdot - 7 + 6 (\sqrt[3]{y} - 7)$

Step 1.3

Apply the distributive property.

$\sqrt[3]{y} \sqrt[3]{y} + \sqrt[3]{y} \cdot - 7 + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $\sqrt[3]{y} \sqrt[3]{y}$ .

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Step 2.1.1.1

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

${\sqrt[3]{y}}^{1} \sqrt[3]{y} + \sqrt[3]{y} \cdot - 7 + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2.1.1.2

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

${\sqrt[3]{y}}^{1} {\sqrt[3]{y}}^{1} + \sqrt[3]{y} \cdot - 7 + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2.1.1.3

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

${\sqrt[3]{y}}^{1 + 1} + \sqrt[3]{y} \cdot - 7 + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2.1.1.4

Add $1$ and $1$ .

${\sqrt[3]{y}}^{2} + \sqrt[3]{y} \cdot - 7 + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2.1.2

Rewrite ${\sqrt[3]{y}}^{2}$ as $\sqrt[3]{y^{2}}$ .

$\sqrt[3]{y^{2}} + \sqrt[3]{y} \cdot - 7 + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2.1.3

Move $- 7$ to the left of $\sqrt[3]{y}$ .

$\sqrt[3]{y^{2}} - 7 \cdot \sqrt[3]{y} + 6 \sqrt[3]{y} + 6 \cdot - 7$

Step 2.1.4

Multiply $6$ by $- 7$ .

$\sqrt[3]{y^{2}} - 7 \sqrt[3]{y} + 6 \sqrt[3]{y} - 42$

Step 2.2

Add $- 7 \sqrt[3]{y}$ and $6 \sqrt[3]{y}$ .

$\sqrt[3]{y^{2}} - \sqrt[3]{y} - 42$