Find the Product (x+1/2)(x-1/2)

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

Step 1

Expand $(x + \frac{1}{2}) (x - \frac{1}{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- \frac{1}{2}) + \frac{1}{2} x + \frac{1}{2} (- \frac{1}{2})$ .

Reorder the factors in the terms $x (- \frac{1}{2})$ and $\frac{1}{2} x$ .

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

Add $- \frac{1}{2} x$ and $\frac{1}{2} x$ .

$x \cdot x + 0 + \frac{1}{2} (- \frac{1}{2})$

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $\frac{1}{2} (- \frac{1}{2})$ .

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Multiply $2$ by $2$ .

$x^{2} - \frac{1}{4}$