Algebra Examples

$(5 \sqrt{2 + 4}) (5 \sqrt{2 - 4})$

Step 1

Simplify by adding and subtracting.

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Step 1.1

Add $2$ and $4$ .

$5 \sqrt{6} (5 \sqrt{2 - 4})$

Step 1.2

Subtract $4$ from $2$ .

$5 \sqrt{6} (5 \sqrt{- 2})$

$5 \sqrt{6} (5 \sqrt{- 2})$

Step 2

Rewrite $- 2$ as $- 1 (2)$ .

$5 \sqrt{6} (5 \sqrt{- 1 (2)})$

Step 3

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$5 \sqrt{6} (5 (\sqrt{- 1} \cdot \sqrt{2}))$

Step 4

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

$5 \sqrt{6} (5 (i \cdot \sqrt{2}))$

Step 5

Multiply $5 \sqrt{6} (5 i \sqrt{2})$ .

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Step 5.1

Multiply $5$ by $5$ .

$25 \sqrt{6} (i \sqrt{2})$

Step 5.2

Combine using the product rule for radicals.

$25 \sqrt{2 \cdot 6} i$

Step 5.3

Multiply $2$ by $6$ .

$25 \sqrt{12} i$

$25 \sqrt{12} i$

Step 6

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 6.1

Factor $4$ out of $12$ .

$25 \sqrt{4 (3)} i$

Step 6.2

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

$25 \sqrt{2^{2} \cdot 3} i$

$25 \sqrt{2^{2} \cdot 3} i$

Step 7

Pull terms out from under the radical.

$25 (2 \sqrt{3}) i$

Step 8

Multiply $2$ by $25$ .

$50 \sqrt{3} i$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$