Algebra Examples

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

Step 1

Apply the distributive property.

$- 2 \sqrt{15} (- 3 \sqrt{3}) - 2 \sqrt{15} (3 \sqrt{5})$

Step 2

Multiply $- 2 \sqrt{15} (- 3 \sqrt{3})$ .

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Step 2.1

Multiply $- 3$ by $- 2$ .

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

Step 2.2

Combine using the product rule for radicals.

$6 \sqrt{3 \cdot 15} - 2 \sqrt{15} (3 \sqrt{5})$

Step 2.3

Multiply $3$ by $15$ .

$6 \sqrt{45} - 2 \sqrt{15} (3 \sqrt{5})$

Step 3

Multiply $- 2 \sqrt{15} (3 \sqrt{5})$ .

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Step 3.1

Multiply $3$ by $- 2$ .

$6 \sqrt{45} - 6 \sqrt{15} \sqrt{5}$

Step 3.2

Combine using the product rule for radicals.

$6 \sqrt{45} - 6 \sqrt{5 \cdot 15}$

Step 3.3

Multiply $5$ by $15$ .

$6 \sqrt{45} - 6 \sqrt{75}$

Step 4

Simplify each term.

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Step 4.1

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 4.1.1

Factor $9$ out of $45$ .

$6 \sqrt{9 (5)} - 6 \sqrt{75}$

Step 4.1.2

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

$6 \sqrt{3^{2} \cdot 5} - 6 \sqrt{75}$

Step 4.2

Pull terms out from under the radical.

$6 (| 3 | \sqrt{5}) - 6 \sqrt{75}$

Step 4.3

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$6 (3 \sqrt{5}) - 6 \sqrt{75}$

Step 4.4

Multiply $3$ by $6$ .

$18 \sqrt{5} - 6 \sqrt{75}$

Step 4.5

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 4.5.1

Factor $25$ out of $75$ .

$18 \sqrt{5} - 6 \sqrt{25 (3)}$

Step 4.5.2

Rewrite $25$ as $5^{2}$ .

$18 \sqrt{5} - 6 \sqrt{5^{2} \cdot 3}$

Step 4.6

Pull terms out from under the radical.

$18 \sqrt{5} - 6 (| 5 | \sqrt{3})$

Step 4.7

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$18 \sqrt{5} - 6 (5 \sqrt{3})$

Step 4.8

Multiply $5$ by $- 6$ .

$18 \sqrt{5} - 30 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{5} - 30 \sqrt{3}$

Decimal Form:

$- 11.71230063 \dots$