Pre-Algebra Examples

$\frac{z^{2} - 16}{4 - z}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16$ as $4^{2}$ .

$\frac{z^{2} - 4^{2}}{4 - z}$

Step 1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = z$ and $b = 4$ .

$\frac{(z + 4) (z - 4)}{4 - z}$

Step 2

Simplify terms.

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Step 2.1

Cancel the common factor of $z - 4$ and $4 - z$ .

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Step 2.1.1

Factor $- 1$ out of $z$ .

$\frac{(z + 4) (- 1 (- z) - 4)}{4 - z}$

Step 2.1.2

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{(z + 4) (- 1 (- z) - 1 (4))}{4 - z}$

Step 2.1.3

Factor $- 1$ out of $- 1 (- z) - 1 (4)$ .

$\frac{(z + 4) (- 1 (- z + 4))}{4 - z}$

Step 2.1.4

Reorder terms.

$\frac{(z + 4) (- 1 (- z + 4))}{- z + 4}$

Step 2.1.5

Cancel the common factor.

$\frac{(z + 4) (- 1 (- z + 4))}{- z + 4}$

Step 2.1.6

Divide $(z + 4) \cdot (- 1)$ by $1$ .

$(z + 4) \cdot (- 1)$

Step 2.2

Simplify by multiplying through.

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Step 2.2.1

Apply the distributive property.

$z \cdot - 1 + 4 \cdot - 1$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

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

$- 1 \cdot z + 4 \cdot - 1$

Step 2.2.2.2

Multiply $4$ by $- 1$ .

$- 1 \cdot z - 4$

Step 2.3

Rewrite $- 1 z$ as $- z$ .

$- z - 4$