Algebra Examples

$(\sqrt{8} - 2 \sqrt{2}) (\sqrt{2} + 2 \sqrt{8})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$(\sqrt{4 (2)} - 2 \sqrt{2}) (\sqrt{2} + 2 \sqrt{8})$

Step 1.1.2

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

$(\sqrt{2^{2} \cdot 2} - 2 \sqrt{2}) (\sqrt{2} + 2 \sqrt{8})$

Step 1.2

Pull terms out from under the radical.

$(2 \sqrt{2} - 2 \sqrt{2}) (\sqrt{2} + 2 \sqrt{8})$

Step 2

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

$0 (\sqrt{2} + 2 \sqrt{8})$

Step 3

Simplify each term.

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Step 3.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 3.1.1

Factor $4$ out of $8$ .

$0 (\sqrt{2} + 2 \sqrt{4 (2)})$

Step 3.1.2

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

$0 (\sqrt{2} + 2 \sqrt{2^{2} \cdot 2})$

Step 3.2

Pull terms out from under the radical.

$0 (\sqrt{2} + 2 (2 \sqrt{2}))$

Step 3.3

Multiply $2$ by $2$ .

$0 (\sqrt{2} + 4 \sqrt{2})$

Step 4

Add $\sqrt{2}$ and $4 \sqrt{2}$ .

$0 (5 \sqrt{2})$

Step 5

Multiply $0 (5 \sqrt{2})$ .

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Step 5.1

Multiply $5$ by $0$ .

$0 \sqrt{2}$

Step 5.2

Multiply $0$ by $\sqrt{2}$ .

$0$