Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x \cdot x + x \frac{5}{2} - \frac{5}{2} x - \frac{5}{2} \cdot \frac{5}{2}$ .

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Step 2.1.1

Reorder the factors in the terms $x \frac{5}{2}$ and $- \frac{5}{2} x$ .

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

Step 2.1.2

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

$x \cdot x + 0 - \frac{5}{2} \cdot \frac{5}{2}$

Step 2.1.3

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

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Multiply $- \frac{5}{2} \cdot \frac{5}{2}$ .

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Step 2.2.2.1

Multiply $\frac{5}{2}$ by $\frac{5}{2}$ .

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

Step 2.2.2.2

Multiply $5$ by $5$ .

$x^{2} - \frac{25}{2 \cdot 2}$

Step 2.2.2.3

Multiply $2$ by $2$ .

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