Algebra Examples

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

Step 1

Rewrite ${(2 + \sqrt{6 x})}^{2}$ as $(2 + \sqrt{6 x}) (2 + \sqrt{6 x})$ .

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

Step 2

Expand $(2 + \sqrt{6 x}) (2 + \sqrt{6 x})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

$2 \cdot 2 + 2 \sqrt{6 x} + \sqrt{6 x} \cdot 2 + \sqrt{6 x} \sqrt{6 x}$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $2$ by $2$ .

$4 + 2 \sqrt{6 x} + \sqrt{6 x} \cdot 2 + \sqrt{6 x} \sqrt{6 x}$

Step 3.1.2

Move $2$ to the left of $\sqrt{6 x}$ .

$4 + 2 \sqrt{6 x} + 2 \cdot \sqrt{6 x} + \sqrt{6 x} \sqrt{6 x}$

Step 3.1.3

Multiply $\sqrt{6 x} \sqrt{6 x}$ .

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Step 3.1.3.1

Raise $\sqrt{6 x}$ to the power of $1$ .

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {\sqrt{6 x}}^{1} \sqrt{6 x}$

Step 3.1.3.2

Raise $\sqrt{6 x}$ to the power of $1$ .

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {\sqrt{6 x}}^{1} {\sqrt{6 x}}^{1}$

Step 3.1.3.3

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

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {\sqrt{6 x}}^{1 + 1}$

Step 3.1.3.4

Add $1$ and $1$ .

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {\sqrt{6 x}}^{2}$

Step 3.1.4

Rewrite ${\sqrt{6 x}}^{2}$ as $6 x$ .

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Step 3.1.4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 x}$ as ${(6 x)}^{\frac{1}{2}}$ .

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {({(6 x)}^{\frac{1}{2}})}^{2}$

Step 3.1.4.2

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

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {(6 x)}^{\frac{1}{2} \cdot 2}$

Step 3.1.4.3

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

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {(6 x)}^{\frac{2}{2}}$

Step 3.1.4.4

Cancel the common factor of $2$ .

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Step 3.1.4.4.1

Cancel the common factor.

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {(6 x)}^{\frac{2}{2}}$

Step 3.1.4.4.2

Rewrite the expression.

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + {(6 x)}^{1}$

Step 3.1.4.5

Simplify.

$4 + 2 \sqrt{6 x} + 2 \sqrt{6 x} + 6 x$

Step 3.2

Add $2 \sqrt{6 x}$ and $2 \sqrt{6 x}$ .

$4 + 4 \sqrt{6 x} + 6 x$

Step 4

Move $4 \sqrt{6 x}$ .

$4 + 6 x + 4 \sqrt{6 x}$

Step 5

Reorder $4$ and $6 x$ .

$6 x + 4 + 4 \sqrt{6 x}$