Simplify ( square root of 8-2 square root of 2)( square root of 2+2 square root of 8)

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

Step 1

Simplify each term.

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

Factor $4$ out of $8$ .

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

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

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

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.

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

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

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

Multiply $5$ by $0$ .

$0 \sqrt{2}$

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

$0$