Finite Math Examples

$(x + \sqrt{2}) (x - 7 \sqrt{2})$

Step 1

Expand $(x + \sqrt{2}) (x - 7 \sqrt{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x (x - 7 \sqrt{2}) + \sqrt{2} (x - 7 \sqrt{2})$

Step 1.2

Apply the distributive property.

$x \cdot x + x (- 7 \sqrt{2}) + \sqrt{2} (x - 7 \sqrt{2})$

Step 1.3

Apply the distributive property.

$x \cdot x + x (- 7 \sqrt{2}) + \sqrt{2} x + \sqrt{2} (- 7 \sqrt{2})$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $x$ by $x$ .

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

Step 2.1.2

Multiply $\sqrt{2} (- 7 \sqrt{2})$ .

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Step 2.1.2.1

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 2.1.2.2

Raise $\sqrt{2}$ to the power of $1$ .

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

Step 2.1.2.3

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

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

Step 2.1.2.4

Add $1$ and $1$ .

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

Step 2.1.3

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

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Step 2.1.3.1

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

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

Step 2.1.3.2

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

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

Step 2.1.3.3

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

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

Step 2.1.3.4

Cancel the common factor of $2$ .

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Step 2.1.3.4.1

Cancel the common factor.

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

Step 2.1.3.4.2

Rewrite the expression.

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

Step 2.1.3.5

Evaluate the exponent.

$x^{2} + x (- 7 \sqrt{2}) + \sqrt{2} x - 7 \cdot 2$

Step 2.1.4

Multiply $- 7$ by $2$ .

$x^{2} + x (- 7 \sqrt{2}) + \sqrt{2} x - 14$

Step 2.2

Reorder the factors of $\sqrt{2} x$ .

$x^{2} + x (- 7 \sqrt{2}) + x \sqrt{2} - 14$

Step 2.3

Add $x (- 7 \sqrt{2})$ and $x \sqrt{2}$ .

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Step 2.3.1

Reorder $x$ and $- 7$ .

$x^{2} - 7 \cdot x \sqrt{2} + x \sqrt{2} - 14$

Step 2.3.2

Add $- 7 \cdot x \sqrt{2}$ and $x \sqrt{2}$ .

$x^{2} - 6 x \sqrt{2} - 14$