Multiply ( square root of 6+7)( square root of 6-7)

$(\sqrt{6} + 7) (\sqrt{6} - 7)$

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

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Apply the distributive property.

$\sqrt{6} (\sqrt{6} - 7) + 7 (\sqrt{6} - 7)$

Apply the distributive property.

$\sqrt{6} \sqrt{6} + \sqrt{6} \cdot - 7 + 7 (\sqrt{6} - 7)$

Apply the distributive property.

$\sqrt{6} \sqrt{6} + \sqrt{6} \cdot - 7 + 7 \sqrt{6} + 7 \cdot - 7$

Simplify and combine like terms.

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Simplify each term.

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Combine using the product rule for radicals.

$\sqrt{6 \cdot 6} + \sqrt{6} \cdot - 7 + 7 \sqrt{6} + 7 \cdot - 7$

Multiply $6$ by $6$ .

$\sqrt{36} + \sqrt{6} \cdot - 7 + 7 \sqrt{6} + 7 \cdot - 7$

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2}} + \sqrt{6} \cdot - 7 + 7 \sqrt{6} + 7 \cdot - 7$

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

$6 + \sqrt{6} \cdot - 7 + 7 \sqrt{6} + 7 \cdot - 7$

Move $- 7$ to the left of $\sqrt{6}$ .

$6 - 7 \cdot \sqrt{6} + 7 \sqrt{6} + 7 \cdot - 7$

Multiply $7$ by $- 7$ .

$6 - 7 \sqrt{6} + 7 \sqrt{6} - 49$

Subtract $49$ from $6$ .

$- 43 - 7 \sqrt{6} + 7 \sqrt{6}$

Add $- 7 \sqrt{6}$ and $7 \sqrt{6}$ .

$- 43 + 0$

Add $- 43$ and $0$ .

$- 43$

Multiply ( square root of 6+7)( square root of 6-7)