Pre-Algebra Examples

${(a - \frac{7}{2})}^{2}$

Step 1

Rewrite ${(a - \frac{7}{2})}^{2}$ as $(a - \frac{7}{2}) (a - \frac{7}{2})$ .

$(a - \frac{7}{2}) (a - \frac{7}{2})$

Step 2

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

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Step 2.1

Apply the distributive property.

$a (a - \frac{7}{2}) - \frac{7}{2} (a - \frac{7}{2})$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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

Multiply $a$ by $a$ .

$a^{2} + a (- \frac{7}{2}) - \frac{7}{2} a - \frac{7}{2} (- \frac{7}{2})$

Step 3.1.2

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

$a^{2} - \frac{a \cdot 7}{2} - \frac{7}{2} a - \frac{7}{2} (- \frac{7}{2})$

Step 3.1.3

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

$a^{2} - \frac{7 \cdot a}{2} - \frac{7}{2} a - \frac{7}{2} (- \frac{7}{2})$

Step 3.1.4

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

$a^{2} - \frac{7 a}{2} - \frac{a \cdot 7}{2} - \frac{7}{2} (- \frac{7}{2})$

Step 3.1.5

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

$a^{2} - \frac{7 a}{2} - \frac{7 \cdot a}{2} - \frac{7}{2} (- \frac{7}{2})$

Step 3.1.6

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

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Step 3.1.6.1

Multiply $- 1$ by $- 1$ .

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

Step 3.1.6.2

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

$a^{2} - \frac{7 a}{2} - \frac{7 a}{2} + \frac{7}{2} \cdot \frac{7}{2}$

Step 3.1.6.3

Multiply $\frac{7}{2}$ by $\frac{7}{2}$ .

$a^{2} - \frac{7 a}{2} - \frac{7 a}{2} + \frac{7 \cdot 7}{2 \cdot 2}$

Step 3.1.6.4

Multiply $7$ by $7$ .

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

Step 3.1.6.5

Multiply $2$ by $2$ .

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

Step 3.2

Subtract $\frac{7 a}{2}$ from $- \frac{7 a}{2}$ .

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

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 $- 2$ .

$a^{2} + 2 (- 1) \frac{7 a}{2} + \frac{49}{4}$

Step 4.1.2

Cancel the common factor.

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

Step 4.1.3

Rewrite the expression.

$a^{2} - 1 (7 a) + \frac{49}{4}$

Step 4.2

Multiply $7$ by $- 1$ .

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