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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

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

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

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

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

Multiply $- 2$ by $2$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

Raise $i$ to the power of $1$ .

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

Raise $i$ to the power of $1$ .

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

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

Multiply $- 4$ by $3$ .

$x^{2} - 12 i^{2}$

Rewrite $i^{2}$ as $- 1$ .

$x^{2} - 12 \cdot - 1$

Multiply $- 12$ by $- 1$ .

$x^{2} + 12$

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

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