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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

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

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

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{2} - 2^{1}$

Evaluate the exponent.

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

Multiply $- 1$ by $2$ .

$x^{2} - 2$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.