Pre-Algebra Examples

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

Step 1

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

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

Step 2

Expand $(2 x - \frac{1}{4}) (2 x - \frac{1}{4})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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

Rewrite using the commutative property of multiplication.

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

Step 3.1.2

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

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Step 3.1.2.1

Move $x$ .

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

Step 3.1.2.2

Multiply $x$ by $x$ .

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

Step 3.1.3

Multiply $2$ by $2$ .

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

Step 3.1.4

Cancel the common factor of $2$ .

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Step 3.1.4.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 3.1.4.2

Factor $2$ out of $2 x$ .

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

Step 3.1.4.3

Factor $2$ out of $4$ .

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

Step 3.1.4.4

Cancel the common factor.

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

Step 3.1.4.5

Rewrite the expression.

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

Step 3.1.5

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

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

Step 3.1.6

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

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

Step 3.1.7

Move the negative in front of the fraction.

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

Step 3.1.8

Cancel the common factor of $2$ .

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Step 3.1.8.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

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

Step 3.1.8.2

Factor $2$ out of $4$ .

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

Step 3.1.8.3

Factor $2$ out of $2 x$ .

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

Step 3.1.8.4

Cancel the common factor.

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

Step 3.1.8.5

Rewrite the expression.

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

Step 3.1.9

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

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

Step 3.1.10

Move the negative in front of the fraction.

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

Step 3.1.11

Multiply $- \frac{1}{4} (- \frac{1}{4})$ .

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Step 3.1.11.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.11.2

Multiply $\frac{1}{4}$ by $1$ .

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

Step 3.1.11.3

Multiply $\frac{1}{4}$ by $\frac{1}{4}$ .

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

Step 3.1.11.4

Multiply $4$ by $4$ .

$4 x^{2} - \frac{x}{2} - \frac{x}{2} + \frac{1}{16}$

Step 3.2

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

$4 x^{2} - 2 \frac{x}{2} + \frac{1}{16}$

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 $- 2$ .

$4 x^{2} + 2 (- 1) \frac{x}{2} + \frac{1}{16}$

Step 4.1.2

Cancel the common factor.

$4 x^{2} + 2 \cdot - 1 \frac{x}{2} + \frac{1}{16}$

Step 4.1.3

Rewrite the expression.

$4 x^{2} - 1 x + \frac{1}{16}$

Step 4.2

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

$4 x^{2} - x + \frac{1}{16}$