Simplify ( square root of 7+9)( square root of 7-9)

$(\sqrt{7} + 9) (\sqrt{7} - 9)$

Step 1

Expand $(\sqrt{7} + 9) (\sqrt{7} - 9)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{7} (\sqrt{7} - 9) + 9 (\sqrt{7} - 9)$

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} \cdot - 9 + 9 (\sqrt{7} - 9)$

Apply the distributive property.

$\sqrt{7} \sqrt{7} + \sqrt{7} \cdot - 9 + 9 \sqrt{7} + 9 \cdot - 9$

Step 2

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{7 \cdot 7} + \sqrt{7} \cdot - 9 + 9 \sqrt{7} + 9 \cdot - 9$

Multiply $7$ by $7$ .

$\sqrt{49} + \sqrt{7} \cdot - 9 + 9 \sqrt{7} + 9 \cdot - 9$

Rewrite $49$ as $7^{2}$ .

$\sqrt{7^{2}} + \sqrt{7} \cdot - 9 + 9 \sqrt{7} + 9 \cdot - 9$

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

$7 + \sqrt{7} \cdot - 9 + 9 \sqrt{7} + 9 \cdot - 9$

Move $- 9$ to the left of $\sqrt{7}$ .

$7 - 9 \cdot \sqrt{7} + 9 \sqrt{7} + 9 \cdot - 9$

Multiply $9$ by $- 9$ .

$7 - 9 \sqrt{7} + 9 \sqrt{7} - 81$

Subtract $81$ from $7$ .

$- 74 - 9 \sqrt{7} + 9 \sqrt{7}$

Add $- 9 \sqrt{7}$ and $9 \sqrt{7}$ .

$- 74 + 0$

Add $- 74$ and $0$ .

$- 74$