Multiply (4- square root of 5)(4+ square root of 5)

$(4 - \sqrt{5}) (4 + \sqrt{5})$

Expand $(4 - \sqrt{5}) (4 + \sqrt{5})$ using the FOIL Method.

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Apply the distributive property.

$4 (4 + \sqrt{5}) - \sqrt{5} (4 + \sqrt{5})$

Apply the distributive property.

$4 \cdot 4 + 4 \sqrt{5} - \sqrt{5} (4 + \sqrt{5})$

Apply the distributive property.

$4 \cdot 4 + 4 \sqrt{5} - \sqrt{5} \cdot 4 - \sqrt{5} \sqrt{5}$

Simplify and combine like terms.

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Simplify each term.

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Multiply $4$ by $4$ .

$16 + 4 \sqrt{5} - \sqrt{5} \cdot 4 - \sqrt{5} \sqrt{5}$

Multiply $4$ by $- 1$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - \sqrt{5} \sqrt{5}$

Multiply $- \sqrt{5} \sqrt{5}$ .

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Raise $\sqrt{5}$ to the power of $1$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - ({\sqrt{5}}^{1} \sqrt{5})$

Raise $\sqrt{5}$ to the power of $1$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - ({\sqrt{5}}^{1} {\sqrt{5}}^{1})$

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

$16 + 4 \sqrt{5} - 4 \sqrt{5} - {\sqrt{5}}^{1 + 1}$

Add $1$ and $1$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - {\sqrt{5}}^{2}$

Rewrite ${\sqrt{5}}^{2}$ as $5$ .

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5}$ as $5^{\frac{1}{2}}$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - {(5^{\frac{1}{2}})}^{2}$

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

$16 + 4 \sqrt{5} - 4 \sqrt{5} - 5^{\frac{1}{2} \cdot 2}$

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

$16 + 4 \sqrt{5} - 4 \sqrt{5} - 5^{\frac{2}{2}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$16 + 4 \sqrt{5} - 4 \sqrt{5} - 5^{\frac{2}{2}}$

Divide $1$ by $1$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - 5^{1}$

Evaluate the exponent.

$16 + 4 \sqrt{5} - 4 \sqrt{5} - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$16 + 4 \sqrt{5} - 4 \sqrt{5} - 5$

Subtract $5$ from $16$ .

$11 + 4 \sqrt{5} - 4 \sqrt{5}$

Subtract $4 \sqrt{5}$ from $4 \sqrt{5}$ .

$11 + 0$

Add $11$ and $0$ .

$11$

Multiply (4- square root of 5)(4+ square root of 5)