Basic Math Examples

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

Step 1

Expand

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

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

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Step 2.1.1

Reorder the factors in the terms

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

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

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

Step 2.1.2

Add

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

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

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

Step 2.1.3

Add

$\sqrt{x} \sqrt{x}$ and

$0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

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

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Step 2.2.1.1

Raise

$\sqrt{x}$ to the power of

$1$ .

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

Step 2.2.1.2

Raise

$\sqrt{x}$ to the power of

$1$ .

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

Step 2.2.1.3

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.1.4

Add

$1$ and

$1$ .

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

Step 2.2.2

Rewrite

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

$x$ .

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Step 2.2.2.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{x}$ as

$x^{\frac{1}{2}}$ .

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

Step 2.2.2.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2.2.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 2.2.2.4

Cancel the common factor of

$2$ .

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Step 2.2.2.4.1

Cancel the common factor.

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

Step 2.2.2.4.2

Rewrite the expression.

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

Step 2.2.2.5

Simplify.

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

Step 2.2.3

Multiply

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

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Step 2.2.3.1

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Step 2.2.3.2

Raise

$\sqrt{3}$ to the power of

$1$ .

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

Step 2.2.3.3

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.2.3.4

Add

$1$ and

$1$ .

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

Step 2.2.4

Rewrite

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

$3$ .

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Step 2.2.4.1

Use

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

$\sqrt{3}$ as

$3^{\frac{1}{2}}$ .

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

Step 2.2.4.2

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2.4.3

Combine

$\frac{1}{2}$ and

$2$ .

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

Step 2.2.4.4

Cancel the common factor of

$2$ .

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Step 2.2.4.4.1

Cancel the common factor.

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

Step 2.2.4.4.2

Rewrite the expression.

$x - 3^{1}$

Step 2.2.4.5

Evaluate the exponent.

$x - 1 \cdot 3$

Step 2.2.5

Multiply

$- 1$ by

$3$ .

$x - 3$