Simplify ( square root of x- square root of 3)( square root of x+ square root of 3)

$(\sqrt{x} - \sqrt{3}) (\sqrt{x} + \sqrt{3})$

Step 1

Expand $(\sqrt{x} - \sqrt{3}) (\sqrt{x} + \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{x} (\sqrt{x} + \sqrt{3}) - \sqrt{3} (\sqrt{x} + \sqrt{3})$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \sqrt{3} - \sqrt{3} (\sqrt{x} + \sqrt{3})$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} \sqrt{3} - \sqrt{3} \sqrt{x} - \sqrt{3} \sqrt{3}$

Step 2

Simplify terms.

Combine the opposite terms in $\sqrt{x} \sqrt{x} + \sqrt{x} \sqrt{3} - \sqrt{3} \sqrt{x} - \sqrt{3} \sqrt{3}$ .

Reorder the factors in the terms $\sqrt{x} \sqrt{3}$ and $- \sqrt{3} \sqrt{x}$ .

$\sqrt{x} \sqrt{x} + \sqrt{3} \sqrt{x} - \sqrt{3} \sqrt{x} - \sqrt{3} \sqrt{3}$

Subtract $\sqrt{3} \sqrt{x}$ from $\sqrt{3} \sqrt{x}$ .

$\sqrt{x} \sqrt{x} + 0 - \sqrt{3} \sqrt{3}$

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

$\sqrt{x} \sqrt{x} - \sqrt{3} \sqrt{3}$

Simplify each term.

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

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

${\sqrt{x}}^{1} \sqrt{x} - \sqrt{3} \sqrt{3}$

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

${\sqrt{x}}^{1} {\sqrt{x}}^{1} - \sqrt{3} \sqrt{3}$

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

${\sqrt{x}}^{1 + 1} - \sqrt{3} \sqrt{3}$

Add $1$ and $1$ .

${\sqrt{x}}^{2} - \sqrt{3} \sqrt{3}$

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

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

${(x^{\frac{1}{2}})}^{2} - \sqrt{3} \sqrt{3}$

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

$x^{\frac{1}{2} \cdot 2} - \sqrt{3} \sqrt{3}$

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

$x^{\frac{2}{2}} - \sqrt{3} \sqrt{3}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{2}{2}} - \sqrt{3} \sqrt{3}$

Rewrite the expression.

$x^{1} - \sqrt{3} \sqrt{3}$

Simplify.

$x - \sqrt{3} \sqrt{3}$

Multiply $- \sqrt{3} \sqrt{3}$ .

Raise $\sqrt{3}$ to the power of $1$ .

$x - ({\sqrt{3}}^{1} \sqrt{3})$

Raise $\sqrt{3}$ to the power of $1$ .

$x - ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$x - {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$x - {\sqrt{3}}^{2}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x - {(3^{\frac{1}{2}})}^{2}$

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

$x - 3^{\frac{1}{2} \cdot 2}$

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

$x - 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x - 3^{\frac{2}{2}}$

Rewrite the expression.

$x - 3^{1}$

Evaluate the exponent.

$x - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$x - 3$

Simplify ( square root of x- square root of 3)( square root of x+ square root of 3)

Related Questions