Simplify (2x-1/2)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move $- 1$ to the left of $x$ .

$4 x^{2} - 1 \cdot x - \frac{1}{2} (2 x) - \frac{1}{2} (- \frac{1}{2})$

Rewrite $- 1 x$ as $- x$ .

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{1}{2}$ into the numerator.

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

Factor $2$ out of $2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $- 1 x$ as $- x$ .

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

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

Multiply $- 1$ by $- 1$ .

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

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

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

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

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

Multiply $2$ by $2$ .

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

Subtract $x$ from $- x$ .

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

Simplify (2x-1/2)^2

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