Basic Math Examples

$(\sqrt[3]{a} - 1) \cdot (\sqrt[3]{a} + 1)$

Step 1

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

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Step 1.1

Apply the distributive property.

$\sqrt[3]{a} (\sqrt[3]{a} + 1) - 1 (\sqrt[3]{a} + 1)$

Step 1.2

Apply the distributive property.

$\sqrt[3]{a} \sqrt[3]{a} + \sqrt[3]{a} \cdot 1 - 1 (\sqrt[3]{a} + 1)$

Step 1.3

Apply the distributive property.

$\sqrt[3]{a} \sqrt[3]{a} + \sqrt[3]{a} \cdot 1 - 1 \sqrt[3]{a} - 1 \cdot 1$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $\sqrt[3]{a} \sqrt[3]{a} + \sqrt[3]{a} \cdot 1 - 1 \sqrt[3]{a} - 1 \cdot 1$ .

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Step 2.1.1

Reorder the factors in the terms $\sqrt[3]{a} \cdot 1$ and $- 1 \sqrt[3]{a}$ .

$\sqrt[3]{a} \sqrt[3]{a} + 1 \sqrt[3]{a} - 1 \sqrt[3]{a} - 1 \cdot 1$

Step 2.1.2

Subtract $1 \sqrt[3]{a}$ from $1 \sqrt[3]{a}$ .

$\sqrt[3]{a} \sqrt[3]{a} + 0 - 1 \cdot 1$

Step 2.1.3

Add $\sqrt[3]{a} \sqrt[3]{a}$ and $0$ .

$\sqrt[3]{a} \sqrt[3]{a} - 1 \cdot 1$

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

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

${\sqrt[3]{a}}^{1} \sqrt[3]{a} - 1 \cdot 1$

Step 2.2.1.2

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

${\sqrt[3]{a}}^{1} {\sqrt[3]{a}}^{1} - 1 \cdot 1$

Step 2.2.1.3

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

${\sqrt[3]{a}}^{1 + 1} - 1 \cdot 1$

Step 2.2.1.4

Add $1$ and $1$ .

${\sqrt[3]{a}}^{2} - 1 \cdot 1$

Step 2.2.2

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

$\sqrt[3]{a^{2}} - 1 \cdot 1$

Step 2.2.3

Multiply $- 1$ by $1$ .

$\sqrt[3]{a^{2}} - 1$