Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

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

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

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

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Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.2.3

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

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

Step 2.2.2.4

Add $1$ and $1$ .

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

Step 2.2.3

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

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Step 2.2.3.1

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

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

Step 2.2.3.2

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

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

Step 2.2.3.3

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

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

Step 2.2.3.4

Cancel the common factor of $2$ .

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Step 2.2.3.4.1

Cancel the common factor.

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

Step 2.2.3.4.2

Rewrite the expression.

$x^{2} - 3^{1}$

Step 2.2.3.5

Evaluate the exponent.

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

Step 2.2.4

Multiply $- 1$ by $3$ .

$x^{2} - 3$