Algebra Examples

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

Step 1

Rewrite ${(4 + x \sqrt{6})}^{2}$ as $(4 + x \sqrt{6}) (4 + x \sqrt{6})$ .

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

Step 2

Expand $(4 + x \sqrt{6}) (4 + x \sqrt{6})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

$4 \cdot 4 + 4 (x \sqrt{6}) + x \sqrt{6} (4 + x \sqrt{6})$

Step 2.3

Apply the distributive property.

$4 \cdot 4 + 4 (x \sqrt{6}) + x \sqrt{6} \cdot 4 + x \sqrt{6} (x \sqrt{6})$

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 $4$ by $4$ .

$16 + 4 (x \sqrt{6}) + x \sqrt{6} \cdot 4 + x \sqrt{6} (x \sqrt{6})$

Step 3.1.2

Move $4$ to the left of $x \sqrt{6}$ .

$16 + 4 x \sqrt{6} + 4 \cdot (x \sqrt{6}) + x \sqrt{6} (x \sqrt{6})$

Step 3.1.3

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

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Step 3.1.3.1

Move $x$ .

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x \cdot x \sqrt{6} \sqrt{6}$

Step 3.1.3.2

Multiply $x$ by $x$ .

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} \sqrt{6} \sqrt{6}$

Step 3.1.4

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

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Step 3.1.4.1

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} ({\sqrt{6}}^{1} \sqrt{6})$

Step 3.1.4.2

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} ({\sqrt{6}}^{1} {\sqrt{6}}^{1})$

Step 3.1.4.3

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} {\sqrt{6}}^{1 + 1}$

Step 3.1.4.4

Add $1$ and $1$ .

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} {\sqrt{6}}^{2}$

Step 3.1.5

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

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Step 3.1.5.1

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} {(6^{\frac{1}{2}})}^{2}$

Step 3.1.5.2

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} \cdot 6^{\frac{1}{2} \cdot 2}$

Step 3.1.5.3

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} \cdot 6^{\frac{2}{2}}$

Step 3.1.5.4

Cancel the common factor of $2$ .

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Step 3.1.5.4.1

Cancel the common factor.

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} \cdot 6^{\frac{2}{2}}$

Step 3.1.5.4.2

Rewrite the expression.

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} \cdot 6^{1}$

Step 3.1.5.5

Evaluate the exponent.

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + x^{2} \cdot 6$

Step 3.1.6

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

$16 + 4 x \sqrt{6} + 4 x \sqrt{6} + 6 x^{2}$

Step 3.2

Add $4 x \sqrt{6}$ and $4 x \sqrt{6}$ .

$16 + 8 x \sqrt{6} + 6 x^{2}$