Basic Math Examples

$(2 + 3 \sqrt{10}) (4 \sqrt{2} - 5)$

Step 1

Expand $(2 + 3 \sqrt{10}) (4 \sqrt{2} - 5)$ using the FOIL Method.

Tap for more steps...

Step 1.1

Apply the distributive property.

$2 (4 \sqrt{2} - 5) + 3 \sqrt{10} (4 \sqrt{2} - 5)$

Step 1.2

Apply the distributive property.

$2 (4 \sqrt{2}) + 2 \cdot - 5 + 3 \sqrt{10} (4 \sqrt{2} - 5)$

Step 1.3

Apply the distributive property.

$2 (4 \sqrt{2}) + 2 \cdot - 5 + 3 \sqrt{10} (4 \sqrt{2}) + 3 \sqrt{10} \cdot - 5$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Multiply $4$ by $2$ .

$8 \sqrt{2} + 2 \cdot - 5 + 3 \sqrt{10} (4 \sqrt{2}) + 3 \sqrt{10} \cdot - 5$

Step 2.2

Multiply $2$ by $- 5$ .

$8 \sqrt{2} - 10 + 3 \sqrt{10} (4 \sqrt{2}) + 3 \sqrt{10} \cdot - 5$

Step 2.3

Multiply $3 \sqrt{10} (4 \sqrt{2})$ .

Tap for more steps...

Step 2.3.1

Multiply $4$ by $3$ .

$8 \sqrt{2} - 10 + 12 \sqrt{10} \sqrt{2} + 3 \sqrt{10} \cdot - 5$

Step 2.3.2

Combine using the product rule for radicals.

$8 \sqrt{2} - 10 + 12 \sqrt{2 \cdot 10} + 3 \sqrt{10} \cdot - 5$

Step 2.3.3

Multiply $2$ by $10$ .

$8 \sqrt{2} - 10 + 12 \sqrt{20} + 3 \sqrt{10} \cdot - 5$

Step 2.4

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

Tap for more steps...

Step 2.4.1

Factor $4$ out of $20$ .

$8 \sqrt{2} - 10 + 12 \sqrt{4 (5)} + 3 \sqrt{10} \cdot - 5$

Step 2.4.2

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

$8 \sqrt{2} - 10 + 12 \sqrt{2^{2} \cdot 5} + 3 \sqrt{10} \cdot - 5$

Step 2.5

Pull terms out from under the radical.

$8 \sqrt{2} - 10 + 12 (2 \sqrt{5}) + 3 \sqrt{10} \cdot - 5$

Step 2.6

Multiply $2$ by $12$ .

$8 \sqrt{2} - 10 + 24 \sqrt{5} + 3 \sqrt{10} \cdot - 5$

Step 2.7

Multiply $- 5$ by $3$ .

$8 \sqrt{2} - 10 + 24 \sqrt{5} - 15 \sqrt{10}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt{2} - 10 + 24 \sqrt{5} - 15 \sqrt{10}$

Decimal Form:

$7.54517505 \dots$