Simplify ( square root of 5-2)( square root of 5+2)

$(\sqrt{5} - 2) (\sqrt{5} + 2)$

Step 1

Expand $(\sqrt{5} - 2) (\sqrt{5} + 2)$ using the FOIL Method.

Apply the distributive property.

$\sqrt{5} (\sqrt{5} + 2) - 2 (\sqrt{5} + 2)$

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot 2 - 2 (\sqrt{5} + 2)$

Apply the distributive property.

$\sqrt{5} \sqrt{5} + \sqrt{5} \cdot 2 - 2 \sqrt{5} - 2 \cdot 2$

Step 2

Simplify and combine like terms.

Simplify each term.

Combine using the product rule for radicals.

$\sqrt{5 \cdot 5} + \sqrt{5} \cdot 2 - 2 \sqrt{5} - 2 \cdot 2$

Multiply $5$ by $5$ .

$\sqrt{25} + \sqrt{5} \cdot 2 - 2 \sqrt{5} - 2 \cdot 2$

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}} + \sqrt{5} \cdot 2 - 2 \sqrt{5} - 2 \cdot 2$

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

$5 + \sqrt{5} \cdot 2 - 2 \sqrt{5} - 2 \cdot 2$

Move $2$ to the left of $\sqrt{5}$ .

$5 + 2 \cdot \sqrt{5} - 2 \sqrt{5} - 2 \cdot 2$

Multiply $- 2$ by $2$ .

$5 + 2 \sqrt{5} - 2 \sqrt{5} - 4$

Subtract $4$ from $5$ .

$1 + 2 \sqrt{5} - 2 \sqrt{5}$

Subtract $2 \sqrt{5}$ from $2 \sqrt{5}$ .

$1 + 0$

Add $1$ and $0$ .

$1$