Finite Math Examples

$(1 + \sqrt{7}) (1 - \sqrt{7})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Expand $(1 + \sqrt{7}) (1 - \sqrt{7})$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$1 (1 - \sqrt{7}) + \sqrt{7} (1 - \sqrt{7})$

Step 1.1.2

Apply the distributive property.

$1 \cdot 1 + 1 (- \sqrt{7}) + \sqrt{7} (1 - \sqrt{7})$

Step 1.1.3

Apply the distributive property.

$1 \cdot 1 + 1 (- \sqrt{7}) + \sqrt{7} \cdot 1 + \sqrt{7} (- \sqrt{7})$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Multiply $1$ by $1$ .

$1 + 1 (- \sqrt{7}) + \sqrt{7} \cdot 1 + \sqrt{7} (- \sqrt{7})$

Step 1.2.1.2

Multiply $- \sqrt{7}$ by $1$ .

$1 - \sqrt{7} + \sqrt{7} \cdot 1 + \sqrt{7} (- \sqrt{7})$

Step 1.2.1.3

Multiply $\sqrt{7}$ by $1$ .

$1 - \sqrt{7} + \sqrt{7} + \sqrt{7} (- \sqrt{7})$

Step 1.2.1.4

Multiply $\sqrt{7} (- \sqrt{7})$ .

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Step 1.2.1.4.1

Raise $\sqrt{7}$ to the power of $1$ .

$1 - \sqrt{7} + \sqrt{7} - ({\sqrt{7}}^{1} \sqrt{7})$

Step 1.2.1.4.2

Raise $\sqrt{7}$ to the power of $1$ .

$1 - \sqrt{7} + \sqrt{7} - ({\sqrt{7}}^{1} {\sqrt{7}}^{1})$

Step 1.2.1.4.3

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

$1 - \sqrt{7} + \sqrt{7} - {\sqrt{7}}^{1 + 1}$

Step 1.2.1.4.4

Add $1$ and $1$ .

$1 - \sqrt{7} + \sqrt{7} - {\sqrt{7}}^{2}$

Step 1.2.1.5

Rewrite ${\sqrt{7}}^{2}$ as $7$ .

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Step 1.2.1.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$1 - \sqrt{7} + \sqrt{7} - {(7^{\frac{1}{2}})}^{2}$

Step 1.2.1.5.2

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

$1 - \sqrt{7} + \sqrt{7} - 7^{\frac{1}{2} \cdot 2}$

Step 1.2.1.5.3

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

$1 - \sqrt{7} + \sqrt{7} - 7^{\frac{2}{2}}$

Step 1.2.1.5.4

Cancel the common factor of $2$ .

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Step 1.2.1.5.4.1

Cancel the common factor.

$1 - \sqrt{7} + \sqrt{7} - 7^{\frac{2}{2}}$

Step 1.2.1.5.4.2

Rewrite the expression.

$1 - \sqrt{7} + \sqrt{7} - 7^{1}$

Step 1.2.1.5.5

Evaluate the exponent.

$1 - \sqrt{7} + \sqrt{7} - 1 \cdot 7$

Step 1.2.1.6

Multiply $- 1$ by $7$ .

$1 - \sqrt{7} + \sqrt{7} - 7$

Step 1.2.2

Subtract $7$ from $1$ .

$- 6 - \sqrt{7} + \sqrt{7}$

Step 1.2.3

Add $- \sqrt{7}$ and $\sqrt{7}$ .

$- 6 + 0$

Step 1.2.4

Add $- 6$ and $0$ .

$- 6$

Step 2

The expression is constant, which means it can be rewritten with a factor of $x^{0}$ . The degree is the largest exponent on the variable.

$0$