Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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Step 2.1

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

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Step 2.1.1

Move $x$ .

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

Step 2.1.2

Multiply $x$ by $x$ .

$x^{2} \sqrt{3} \sqrt{6} + x \sqrt{3} (- 2 x) + x \sqrt{3} \sqrt{3}$

Step 2.2

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

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Step 2.2.1

Move $x$ .

$x^{2} \sqrt{3} \sqrt{6} + x \cdot x \sqrt{3} \cdot - 2 + x \sqrt{3} \sqrt{3}$

Step 2.2.2

Multiply $x$ by $x$ .

$x^{2} \sqrt{3} \sqrt{6} + x^{2} \sqrt{3} \cdot - 2 + x \sqrt{3} \sqrt{3}$

Step 2.3

Multiply $x \sqrt{3} \sqrt{3}$ .

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Step 2.3.1

Raise $\sqrt{3}$ to the power of $1$ .

$x^{2} \sqrt{3} \sqrt{6} + x^{2} \sqrt{3} \cdot - 2 + x ({\sqrt{3}}^{1} \sqrt{3})$

Step 2.3.2

Raise $\sqrt{3}$ to the power of $1$ .

$x^{2} \sqrt{3} \sqrt{6} + x^{2} \sqrt{3} \cdot - 2 + x ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

Step 2.3.3

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

$x^{2} \sqrt{3} \sqrt{6} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{1 + 1}$

Step 2.3.4

Add $1$ and $1$ .

$x^{2} \sqrt{3} \sqrt{6} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{2}$

Step 3

Simplify each term.

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Step 3.1

Multiply $x^{2} \sqrt{3} \sqrt{6}$ .

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Step 3.1.1

Combine using the product rule for radicals.

$x^{2} \sqrt{6 \cdot 3} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{2}$

Step 3.1.2

Multiply $6$ by $3$ .

$x^{2} \sqrt{18} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{2}$

Step 3.2

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

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Step 3.2.1

Factor $9$ out of $18$ .

$x^{2} \sqrt{9 (2)} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{2}$

Step 3.2.2

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

$x^{2} \sqrt{3^{2} \cdot 2} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{2}$

Step 3.3

Pull terms out from under the radical.

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

Step 3.4

Move $3$ to the left of $x^{2}$ .

$3 \cdot x^{2} \sqrt{2} + x^{2} \sqrt{3} \cdot - 2 + x {\sqrt{3}}^{2}$

Step 3.5

Move $- 2$ to the left of $x^{2} \sqrt{3}$ .

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

Step 3.6

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 3.6.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 3.6.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3 x^{2} \sqrt{2} - 2 x^{2} \sqrt{3} + x \cdot 3^{\frac{1}{2} \cdot 2}$

Step 3.6.3

Combine $\frac{1}{2}$ and $2$ .

$3 x^{2} \sqrt{2} - 2 x^{2} \sqrt{3} + x \cdot 3^{\frac{2}{2}}$

Step 3.6.4

Cancel the common factor of $2$ .

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Step 3.6.4.1

Cancel the common factor.

$3 x^{2} \sqrt{2} - 2 x^{2} \sqrt{3} + x \cdot 3^{\frac{2}{2}}$

Step 3.6.4.2

Rewrite the expression.

$3 x^{2} \sqrt{2} - 2 x^{2} \sqrt{3} + x \cdot 3^{1}$

Step 3.6.5

Evaluate the exponent.

$3 x^{2} \sqrt{2} - 2 x^{2} \sqrt{3} + x \cdot 3$

Step 3.7

Move $3$ to the left of $x$ .

$3 x^{2} \sqrt{2} - 2 x^{2} \sqrt{3} + 3 x$