Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

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.

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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.

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

Step 2.1.2

Multiply $5$ by $5$ .

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

Step 2.1.3

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

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

Step 2.1.4

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

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

Step 2.1.5

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

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

Step 2.1.6

Multiply $- 2$ by $2$ .

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

Step 2.2

Subtract $4$ from $5$ .

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

Step 2.3

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

$1 + 0$

Step 2.4

Add $1$ and $0$ .

$1$