Pre-Algebra Examples

$(\sqrt{13} + 7) (\sqrt{13} - 7)$

Step 1

Expand $(\sqrt{13} + 7) (\sqrt{13} - 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{13} (\sqrt{13} - 7) + 7 (\sqrt{13} - 7)$

Step 1.2

Apply the distributive property.

$\sqrt{13} \sqrt{13} + \sqrt{13} \cdot - 7 + 7 (\sqrt{13} - 7)$

Step 1.3

Apply the distributive property.

$\sqrt{13} \sqrt{13} + \sqrt{13} \cdot - 7 + 7 \sqrt{13} + 7 \cdot - 7$

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

Combine using the product rule for radicals.

$\sqrt{13 \cdot 13} + \sqrt{13} \cdot - 7 + 7 \sqrt{13} + 7 \cdot - 7$

Step 2.1.2

Multiply $13$ by $13$ .

$\sqrt{169} + \sqrt{13} \cdot - 7 + 7 \sqrt{13} + 7 \cdot - 7$

Step 2.1.3

Rewrite $169$ as $13^{2}$ .

$\sqrt{13^{2}} + \sqrt{13} \cdot - 7 + 7 \sqrt{13} + 7 \cdot - 7$

Step 2.1.4

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

$13 + \sqrt{13} \cdot - 7 + 7 \sqrt{13} + 7 \cdot - 7$

Step 2.1.5

Move $- 7$ to the left of $\sqrt{13}$ .

$13 - 7 \cdot \sqrt{13} + 7 \sqrt{13} + 7 \cdot - 7$

Step 2.1.6

Multiply $7$ by $- 7$ .

$13 - 7 \sqrt{13} + 7 \sqrt{13} - 49$

Step 2.2

Subtract $49$ from $13$ .

$- 36 - 7 \sqrt{13} + 7 \sqrt{13}$

Step 2.3

Add $- 7 \sqrt{13}$ and $7 \sqrt{13}$ .

$- 36 + 0$

Step 2.4

Add $- 36$ and $0$ .

$- 36$