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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

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

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

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

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

Multiply $- 2$ by $2$ .

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

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

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

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

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

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

$x^{2} - 4 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $- 4$ by $3$ .

$x^{2} - 12$

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

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