Basic Math Examples

$(\sqrt{3} - 1) (\sqrt{3} + 1)$

Step 1

Expand $(\sqrt{3} - 1) (\sqrt{3} + 1)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$\sqrt{3} (\sqrt{3} + 1) - 1 (\sqrt{3} + 1)$

Step 1.2

Apply the distributive property.

$\sqrt{3} \sqrt{3} + \sqrt{3} \cdot 1 - 1 (\sqrt{3} + 1)$

Step 1.3

Apply the distributive property.

$\sqrt{3} \sqrt{3} + \sqrt{3} \cdot 1 - 1 \sqrt{3} - 1 \cdot 1$

Step 2

Simplify and combine like terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 3} + \sqrt{3} \cdot 1 - 1 \sqrt{3} - 1 \cdot 1$

Step 2.1.2

Multiply $3$ by $3$ .

$\sqrt{9} + \sqrt{3} \cdot 1 - 1 \sqrt{3} - 1 \cdot 1$

Step 2.1.3

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2}} + \sqrt{3} \cdot 1 - 1 \sqrt{3} - 1 \cdot 1$

Step 2.1.4

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

$3 + \sqrt{3} \cdot 1 - 1 \sqrt{3} - 1 \cdot 1$

Step 2.1.5

Multiply $\sqrt{3}$ by $1$ .

$3 + \sqrt{3} - 1 \sqrt{3} - 1 \cdot 1$

Step 2.1.6

Rewrite $- 1 \sqrt{3}$ as $- \sqrt{3}$ .

$3 + \sqrt{3} - \sqrt{3} - 1 \cdot 1$

Step 2.1.7

Multiply $- 1$ by $1$ .

$3 + \sqrt{3} - \sqrt{3} - 1$

Step 2.2

Subtract $1$ from $3$ .

$2 + \sqrt{3} - \sqrt{3}$

Step 2.3

Subtract $\sqrt{3}$ from $\sqrt{3}$ .

$2 + 0$

Step 2.4

Add $2$ and $0$ .

$2$