Calculus Examples

$(5 \sqrt{10} + 4) (2 \sqrt{2} - 1)$

Step 1

Expand $(5 \sqrt{10} + 4) (2 \sqrt{2} - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 \sqrt{10} (2 \sqrt{2} - 1) + 4 (2 \sqrt{2} - 1)$

Step 1.2

Apply the distributive property.

$5 \sqrt{10} (2 \sqrt{2}) + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2} - 1)$

Step 1.3

Apply the distributive property.

$5 \sqrt{10} (2 \sqrt{2}) + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2

Simplify each term.

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Step 2.1

Multiply $5 \sqrt{10} (2 \sqrt{2})$ .

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Step 2.1.1

Multiply $2$ by $5$ .

$10 \sqrt{10} \sqrt{2} + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.1.2

Combine using the product rule for radicals.

$10 \sqrt{2 \cdot 10} + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.1.3

Multiply $2$ by $10$ .

$10 \sqrt{20} + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.2

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 2.2.1

Factor $4$ out of $20$ .

$10 \sqrt{4 (5)} + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.2.2

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

$10 \sqrt{2^{2} \cdot 5} + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.3

Pull terms out from under the radical.

$10 (2 \sqrt{5}) + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.4

Multiply $2$ by $10$ .

$20 \sqrt{5} + 5 \sqrt{10} \cdot - 1 + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.5

Multiply $- 1$ by $5$ .

$20 \sqrt{5} - 5 \sqrt{10} + 4 (2 \sqrt{2}) + 4 \cdot - 1$

Step 2.6

Multiply $2$ by $4$ .

$20 \sqrt{5} - 5 \sqrt{10} + 8 \sqrt{2} + 4 \cdot - 1$

Step 2.7

Multiply $4$ by $- 1$ .

$20 \sqrt{5} - 5 \sqrt{10} + 8 \sqrt{2} - 4$

Step 3

The result can be shown in multiple forms.

Exact Form:

$20 \sqrt{5} - 5 \sqrt{10} + 8 \sqrt{2} - 4$

Decimal Form:

$36.22367974 \dots$