Algebra Examples

$(3 x \sqrt{2 x}) (4 x \sqrt{3 x^{3}})$

Step 1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1

Move $x$ .

$3 (x \cdot x) \sqrt{2 x} (4 \sqrt{3 x^{3}})$

Step 1.2

Multiply $x$ by $x$ .

$3 x^{2} \sqrt{2 x} (4 \sqrt{3 x^{3}})$

$3 x^{2} \sqrt{2 x} (4 \sqrt{3 x^{3}})$

Step 2

Rewrite $3 x^{3}$ as $x^{2} \cdot (3 x)$ .

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Step 2.1

Factor out $x^{2}$ .

$3 x^{2} \sqrt{2 x} (4 \sqrt{3 (x^{2} x)})$

Step 2.2

Reorder $3$ and $x^{2}$ .

$3 x^{2} \sqrt{2 x} (4 \sqrt{x^{2} \cdot 3 x})$

Step 2.3

Add parentheses.

$3 x^{2} \sqrt{2 x} (4 \sqrt{x^{2} \cdot (3 x)})$

$3 x^{2} \sqrt{2 x} (4 \sqrt{x^{2} \cdot (3 x)})$

Step 3

Pull terms out from under the radical.

$3 x^{2} \sqrt{2 x} (4 (x \sqrt{3 x}))$

Step 4

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.1

Move $x$ .

$3 (x \cdot x^{2}) \sqrt{2 x} (4 (\sqrt{3 x}))$

Step 4.2

Multiply $x$ by $x^{2}$ .

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Step 4.2.1

Raise $x$ to the power of $1$ .

$3 (x^{1} x^{2}) \sqrt{2 x} (4 (\sqrt{3 x}))$

Step 4.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{1 + 2} \sqrt{2 x} (4 (\sqrt{3 x}))$

$3 x^{1 + 2} \sqrt{2 x} (4 (\sqrt{3 x}))$

Step 4.3

Add $1$ and $2$ .

$3 x^{3} \sqrt{2 x} (4 (\sqrt{3 x}))$

$3 x^{3} \sqrt{2 x} (4 (\sqrt{3 x}))$

Step 5

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

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Step 5.1

Multiply $4$ by $3$ .

$12 x^{3} \sqrt{2 x} \sqrt{3 x}$

Step 5.2

Combine using the product rule for radicals.

$12 x^{3} \sqrt{3 x (2 x)}$

Step 5.3

Multiply $2$ by $3$ .

$12 x^{3} \sqrt{6 x \cdot x}$

Step 5.4

Raise $x$ to the power of $1$ .

$12 x^{3} \sqrt{6 (x^{1} x)}$

Step 5.5

Raise $x$ to the power of $1$ .

$12 x^{3} \sqrt{6 (x^{1} x^{1})}$

Step 5.6

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 x^{3} \sqrt{6 x^{1 + 1}}$

Step 5.7

Add $1$ and $1$ .

$12 x^{3} \sqrt{6 x^{2}}$

$12 x^{3} \sqrt{6 x^{2}}$

Step 6

Reorder $6$ and $x^{2}$ .

$12 x^{3} \sqrt{x^{2} \cdot 6}$

Step 7

Pull terms out from under the radical.

$12 x^{3} (x \sqrt{6})$

Step 8

Multiply $x^{3}$ by $x$ by adding the exponents.

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Step 8.1

Move $x$ .

$12 (x \cdot x^{3}) \sqrt{6}$

Step 8.2

Multiply $x$ by $x^{3}$ .

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Step 8.2.1

Raise $x$ to the power of $1$ .

$12 (x^{1} x^{3}) \sqrt{6}$

Step 8.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$12 x^{1 + 3} \sqrt{6}$

$12 x^{1 + 3} \sqrt{6}$

Step 8.3

Add $1$ and $3$ .

$12 x^{4} \sqrt{6}$

$12 x^{4} \sqrt{6}$

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