Pre-Algebra Examples

$(7 x - \frac{1}{2}) (7 x + \frac{1}{2})$

Step 1

Expand $(7 x - \frac{1}{2}) (7 x + \frac{1}{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 x (7 x + \frac{1}{2}) - \frac{1}{2} (7 x + \frac{1}{2})$

Step 1.2

Apply the distributive property.

$7 x (7 x) + 7 x \frac{1}{2} - \frac{1}{2} (7 x + \frac{1}{2})$

Step 1.3

Apply the distributive property.

$7 x (7 x) + 7 x \frac{1}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$7 \cdot 7 x \cdot x + 7 x \frac{1}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$7 \cdot 7 (x \cdot x) + 7 x \frac{1}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.2.2

Multiply $x$ by $x$ .

$7 \cdot 7 x^{2} + 7 x \frac{1}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.3

Multiply $7$ by $7$ .

$49 x^{2} + 7 x \frac{1}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.4

Multiply $7 x \frac{1}{2}$ .

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Step 2.1.4.1

Combine $7$ and $\frac{1}{2}$ .

$49 x^{2} + x \frac{7}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.4.2

Combine $x$ and $\frac{7}{2}$ .

$49 x^{2} + \frac{x \cdot 7}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.5

Move $7$ to the left of $x$ .

$49 x^{2} + \frac{7 \cdot x}{2} - \frac{1}{2} (7 x) - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.6

Multiply $- \frac{1}{2} (7 x)$ .

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Step 2.1.6.1

Multiply $7$ by $- 1$ .

$49 x^{2} + \frac{7 x}{2} - 7 (\frac{1}{2}) x - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.6.2

Combine $- 7$ and $\frac{1}{2}$ .

$49 x^{2} + \frac{7 x}{2} + \frac{- 7}{2} x - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.6.3

Combine $\frac{- 7}{2}$ and $x$ .

$49 x^{2} + \frac{7 x}{2} + \frac{- 7 x}{2} - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.7

Move the negative in front of the fraction.

$49 x^{2} + \frac{7 x}{2} - \frac{7 x}{2} - \frac{1}{2} \cdot \frac{1}{2}$

Step 2.1.8

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

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Step 2.1.8.1

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

$49 x^{2} + \frac{7 x}{2} - \frac{7 x}{2} - \frac{1}{2 \cdot 2}$

Step 2.1.8.2

Multiply $2$ by $2$ .

$49 x^{2} + \frac{7 x}{2} - \frac{7 x}{2} - \frac{1}{4}$

Step 2.2

Subtract $\frac{7 x}{2}$ from $\frac{7 x}{2}$ .

$49 x^{2} + 0 - \frac{1}{4}$

Step 2.3

Add $49 x^{2}$ and $0$ .

$49 x^{2} - \frac{1}{4}$