Finite Math Examples

${(\frac{1}{2} x - 5)}^{2}$

Step 1

Combine fractions.

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Step 1.1

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

${(\frac{x}{2} - 5)}^{2}$

Step 1.2

Rewrite ${(\frac{x}{2} - 5)}^{2}$ as $(\frac{x}{2} - 5) (\frac{x}{2} - 5)$ .

$(\frac{x}{2} - 5) (\frac{x}{2} - 5)$

Step 2

Expand $(\frac{x}{2} - 5) (\frac{x}{2} - 5)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$\frac{x}{2} (\frac{x}{2} - 5) - 5 (\frac{x}{2} - 5)$

Step 2.2

Apply the distributive property.

$\frac{x}{2} \cdot \frac{x}{2} + \frac{x}{2} \cdot - 5 - 5 (\frac{x}{2} - 5)$

Step 2.3

Apply the distributive property.

$\frac{x}{2} \cdot \frac{x}{2} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $\frac{x}{2} \cdot \frac{x}{2}$ .

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Step 3.1.1.1

Multiply $\frac{x}{2}$ by $\frac{x}{2}$ .

$\frac{x \cdot x}{2 \cdot 2} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.1.2

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

$\frac{x^{1} x}{2 \cdot 2} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.1.3

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

$\frac{x^{1} x^{1}}{2 \cdot 2} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.1.4

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

$\frac{x^{1 + 1}}{2 \cdot 2} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.1.5

Add $1$ and $1$ .

$\frac{x^{2}}{2 \cdot 2} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.1.6

Multiply $2$ by $2$ .

$\frac{x^{2}}{4} + \frac{x}{2} \cdot - 5 - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.2

Combine $\frac{x}{2}$ and $- 5$ .

$\frac{x^{2}}{4} + \frac{x \cdot - 5}{2} - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.3

Move $- 5$ to the left of $x$ .

$\frac{x^{2}}{4} + \frac{- 5 \cdot x}{2} - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.4

Move the negative in front of the fraction.

$\frac{x^{2}}{4} - \frac{5 \cdot x}{2} - 5 \frac{x}{2} - 5 \cdot - 5$

Step 3.1.5

Combine $- 5$ and $\frac{x}{2}$ .

$\frac{x^{2}}{4} - \frac{5 x}{2} + \frac{- 5 x}{2} - 5 \cdot - 5$

Step 3.1.6

Move the negative in front of the fraction.

$\frac{x^{2}}{4} - \frac{5 x}{2} - \frac{5 x}{2} - 5 \cdot - 5$

Step 3.1.7

Multiply $- 5$ by $- 5$ .

$\frac{x^{2}}{4} - \frac{5 x}{2} - \frac{5 x}{2} + 25$

Step 3.2

Subtract $\frac{5 x}{2}$ from $- \frac{5 x}{2}$ .

$\frac{x^{2}}{4} - 2 \frac{5 x}{2} + 25$

Step 4

Simplify each term.

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Step 4.1

Cancel the common factor of $2$ .

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Step 4.1.1

Factor $2$ out of $- 2$ .

$\frac{x^{2}}{4} + 2 (- 1) \frac{5 x}{2} + 25$

Step 4.1.2

Cancel the common factor.

$\frac{x^{2}}{4} + 2 \cdot - 1 \frac{5 x}{2} + 25$

Step 4.1.3

Rewrite the expression.

$\frac{x^{2}}{4} - 1 (5 x) + 25$

Step 4.2

Multiply $5$ by $- 1$ .

$\frac{x^{2}}{4} - 5 x + 25$