Basic Math Examples

$(2 \sqrt{3} - 5) (3 + 4 \sqrt{6})$

Step 1

Expand $(2 \sqrt{3} - 5) (3 + 4 \sqrt{6})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 \sqrt{3} (3 + 4 \sqrt{6}) - 5 (3 + 4 \sqrt{6})$

Step 1.2

Apply the distributive property.

$2 \sqrt{3} \cdot 3 + 2 \sqrt{3} (4 \sqrt{6}) - 5 (3 + 4 \sqrt{6})$

Step 1.3

Apply the distributive property.

$2 \sqrt{3} \cdot 3 + 2 \sqrt{3} (4 \sqrt{6}) - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2

Simplify each term.

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Step 2.1

Multiply $3$ by $2$ .

$6 \sqrt{3} + 2 \sqrt{3} (4 \sqrt{6}) - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.2

Multiply $2 \sqrt{3} (4 \sqrt{6})$ .

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Step 2.2.1

Multiply $4$ by $2$ .

$6 \sqrt{3} + 8 \sqrt{3} \sqrt{6} - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.2.2

Combine using the product rule for radicals.

$6 \sqrt{3} + 8 \sqrt{6 \cdot 3} - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.2.3

Multiply $6$ by $3$ .

$6 \sqrt{3} + 8 \sqrt{18} - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.3

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 2.3.1

Factor $9$ out of $18$ .

$6 \sqrt{3} + 8 \sqrt{9 (2)} - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.3.2

Rewrite $9$ as $3^{2}$ .

$6 \sqrt{3} + 8 \sqrt{3^{2} \cdot 2} - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.4

Pull terms out from under the radical.

$6 \sqrt{3} + 8 (3 \sqrt{2}) - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.5

Multiply $3$ by $8$ .

$6 \sqrt{3} + 24 \sqrt{2} - 5 \cdot 3 - 5 (4 \sqrt{6})$

Step 2.6

Multiply $- 5$ by $3$ .

$6 \sqrt{3} + 24 \sqrt{2} - 15 - 5 (4 \sqrt{6})$

Step 2.7

Multiply $4$ by $- 5$ .

$6 \sqrt{3} + 24 \sqrt{2} - 15 - 20 \sqrt{6}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt{3} + 24 \sqrt{2} - 15 - 20 \sqrt{6}$

Decimal Form:

$- 19.65636451 \dots$