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

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

Step 1

Rewrite ${(x + \frac{1}{2})}^{2}$ as $(x + \frac{1}{2}) (x + \frac{1}{2})$ .

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

Step 2

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.

$x \cdot x + x \frac{1}{2} + \frac{1}{2} x + \frac{1}{2} \cdot \frac{1}{2}$

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

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

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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