Simplify the Radical Expression (2+ square root of 6)(2- square root of 6)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$4 + 2 (- \sqrt{6}) + \sqrt{6} \cdot 2 + \sqrt{6} (- \sqrt{6})$

Multiply $- 1$ by $2$ .

$4 - 2 \sqrt{6} + \sqrt{6} \cdot 2 + \sqrt{6} (- \sqrt{6})$

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

$4 - 2 \sqrt{6} + 2 \cdot \sqrt{6} + \sqrt{6} (- \sqrt{6})$

Multiply $\sqrt{6} (- \sqrt{6})$ .

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

$4 - 2 \sqrt{6} + 2 \sqrt{6} - 6^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 - 2 \sqrt{6} + 2 \sqrt{6} - 6^{\frac{2}{2}}$

Rewrite the expression.

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

Evaluate the exponent.

$4 - 2 \sqrt{6} + 2 \sqrt{6} - 1 \cdot 6$

Multiply $- 1$ by $6$ .

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

Subtract $6$ from $4$ .

$- 2 - 2 \sqrt{6} + 2 \sqrt{6}$

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

$- 2 + 0$

Add $- 2$ and $0$ .

$- 2$

Simplify the Radical Expression (2+ square root of 6)(2- square root of 6)

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