Algebra Examples

Simplify $(\sqrt{14} - 3) (\sqrt{14} + 5)$

Step 1

Expand $(\sqrt{14} - 3) (\sqrt{14} + 5)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{14} (\sqrt{14} + 5) - 3 (\sqrt{14} + 5)$

Step 1.2

Apply the distributive property.

$\sqrt{14} \sqrt{14} + \sqrt{14} \cdot 5 - 3 (\sqrt{14} + 5)$

Step 1.3

Apply the distributive property.

$\sqrt{14} \sqrt{14} + \sqrt{14} \cdot 5 - 3 \sqrt{14} - 3 \cdot 5$

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.

$\sqrt{14 \cdot 14} + \sqrt{14} \cdot 5 - 3 \sqrt{14} - 3 \cdot 5$

Step 2.1.2

Multiply $14$ by $14$ .

$\sqrt{196} + \sqrt{14} \cdot 5 - 3 \sqrt{14} - 3 \cdot 5$

Step 2.1.3

Rewrite $196$ as $14^{2}$ .

$\sqrt{14^{2}} + \sqrt{14} \cdot 5 - 3 \sqrt{14} - 3 \cdot 5$

Step 2.1.4

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

$14 + \sqrt{14} \cdot 5 - 3 \sqrt{14} - 3 \cdot 5$

Step 2.1.5

Move $5$ to the left of $\sqrt{14}$ .

$14 + 5 \cdot \sqrt{14} - 3 \sqrt{14} - 3 \cdot 5$

Step 2.1.6

Multiply $- 3$ by $5$ .

$14 + 5 \sqrt{14} - 3 \sqrt{14} - 15$

Step 2.2

Subtract $15$ from $14$ .

$- 1 + 5 \sqrt{14} - 3 \sqrt{14}$

Step 2.3

Subtract $3 \sqrt{14}$ from $5 \sqrt{14}$ .

$- 1 + 2 \sqrt{14}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 1 + 2 \sqrt{14}$

Decimal Form:

$6.48331477 \dots$