Simplify ( square root of x+ square root of 2)( square root of x- square root of 2)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $\sqrt{x} \sqrt{x} + \sqrt{x} (- \sqrt{2}) + \sqrt{2} \sqrt{x} + \sqrt{2} (- \sqrt{2})$ .

Reorder the factors in the terms $\sqrt{x} (- \sqrt{2})$ and $\sqrt{2} \sqrt{x}$ .

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

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

$\sqrt{x} \sqrt{x} + 0 + \sqrt{2} (- \sqrt{2})$

Add $\sqrt{x} \sqrt{x}$ and $0$ .

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

Simplify each term.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Multiply $\sqrt{2} (- \sqrt{2})$ .

Raise $\sqrt{2}$ to the power of $1$ .

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

Raise $\sqrt{2}$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

$x - 2^{\frac{1}{2} \cdot 2}$

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

$x - 2^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x - 2^{\frac{2}{2}}$

Rewrite the expression.

$x - 2^{1}$

Evaluate the exponent.

$x - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$x - 2$

Simplify ( square root of x+ square root of 2)( square root of x- square root of 2)

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