Algebra Examples

$(\sqrt{2} - 7) (\sqrt{2} + 7)$

Step 1

Expand $(\sqrt{2} - 7) (\sqrt{2} + 7)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$\sqrt{2} (\sqrt{2} + 7) - 7 (\sqrt{2} + 7)$

Step 1.2

Apply the distributive property.

$\sqrt{2} \sqrt{2} + \sqrt{2} \cdot 7 - 7 (\sqrt{2} + 7)$

Step 1.3

Apply the distributive property.

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

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.

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

Step 2.1.2

Multiply $2$ by $2$ .

$\sqrt{4} + \sqrt{2} \cdot 7 - 7 \sqrt{2} - 7 \cdot 7$

Step 2.1.3

Rewrite $4$ as $2^{2}$ .

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

Step 2.1.4

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

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

Step 2.1.5

Move $7$ to the left of $\sqrt{2}$ .

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

Step 2.1.6

Multiply $- 7$ by $7$ .

$2 + 7 \sqrt{2} - 7 \sqrt{2} - 49$

Step 2.2

Subtract $49$ from $2$ .

$- 47 + 7 \sqrt{2} - 7 \sqrt{2}$

Step 2.3

Subtract $7 \sqrt{2}$ from $7 \sqrt{2}$ .

$- 47 + 0$

Step 2.4

Add $- 47$ and $0$ .

$- 47$