Simplify ( square root of x+2 square root of 3)( square root of x-2 square root of 3)

$(\sqrt{x} + 2 \sqrt{3}) (\sqrt{x} - 2 \sqrt{3})$

Step 1

Expand $(\sqrt{x} + 2 \sqrt{3}) (\sqrt{x} - 2 \sqrt{3})$ using the FOIL Method.

Apply the distributive property.

$\sqrt{x} (\sqrt{x} - 2 \sqrt{3}) + 2 \sqrt{3} (\sqrt{x} - 2 \sqrt{3})$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} (- 2 \sqrt{3}) + 2 \sqrt{3} (\sqrt{x} - 2 \sqrt{3})$

Apply the distributive property.

$\sqrt{x} \sqrt{x} + \sqrt{x} (- 2 \sqrt{3}) + 2 \sqrt{3} \sqrt{x} + 2 \sqrt{3} (- 2 \sqrt{3})$

Step 2

Simplify terms.

Combine the opposite terms in $\sqrt{x} \sqrt{x} + \sqrt{x} (- 2 \sqrt{3}) + 2 \sqrt{3} \sqrt{x} + 2 \sqrt{3} (- 2 \sqrt{3})$ .

Reorder the factors in the terms $\sqrt{x} (- 2 \sqrt{3})$ and $2 \sqrt{3} \sqrt{x}$ .

$\sqrt{x} \sqrt{x} - 2 \sqrt{3} \sqrt{x} + 2 \sqrt{3} \sqrt{x} + 2 \sqrt{3} (- 2 \sqrt{3})$

Add $- 2 \sqrt{3} \sqrt{x}$ and $2 \sqrt{3} \sqrt{x}$ .

$\sqrt{x} \sqrt{x} + 0 + 2 \sqrt{3} (- 2 \sqrt{3})$

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

$\sqrt{x} \sqrt{x} + 2 \sqrt{3} (- 2 \sqrt{3})$

Simplify each term.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x + 2 \sqrt{3} (- 2 \sqrt{3})$

Multiply $2 \sqrt{3} (- 2 \sqrt{3})$ .

Multiply $- 2$ by $2$ .

$x - 4 \sqrt{3} \sqrt{3}$

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

$x - 4 ({\sqrt{3}}^{1} \sqrt{3})$

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

$x - 4 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})$

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

$x - 4 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$x - 4 {\sqrt{3}}^{2}$

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

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

$x - 4 {(3^{\frac{1}{2}})}^{2}$

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

$x - 4 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$x - 4 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x - 4 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$x - 4 \cdot 3^{1}$

Evaluate the exponent.

$x - 4 \cdot 3$

Multiply $- 4$ by $3$ .

$x - 12$

Simplify ( square root of x+2 square root of 3)( square root of x-2 square root of 3)

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