Pre-Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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

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 $a = y$ and $b = 4$ .

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

Step 2

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

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Step 2.1

Factor $- 1$ out of $y$ .

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

Step 2.2

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

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

Step 2.3

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

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

Step 2.4

Reorder terms.

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

Step 2.5

Cancel the common factor.

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

Step 2.6

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

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

Step 3

Apply the distributive property.

$y \cdot - 1 + 4 \cdot - 1$

Step 4

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

$- 1 \cdot y + 4 \cdot - 1$

Step 5

Multiply $4$ by $- 1$ .

$- 1 \cdot y - 4$

Step 6

Rewrite $- 1 y$ as $- y$ .

$- y - 4$