Divide (4x^2-16)/(2-x)

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

Step 1

Simplify the numerator.

Factor $4$ out of $4 x^{2} - 16$ .

Factor $4$ out of $4 x^{2}$ .

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

Factor $4$ out of $- 16$ .

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

Factor $4$ out of $4 x^{2} + 4 \cdot - 4$ .

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

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

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

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

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

Step 2

Cancel the common factor of $x - 2$ and $2 - x$ .

Factor $- 1$ out of $x$ .

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

Rewrite $- 2$ as $- 1 (2)$ .

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

Factor $- 1$ out of $- 1 (- x) - 1 (2)$ .

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

Reorder terms.

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

Cancel the common factor.

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

Divide $4 (x + 2) \cdot (- 1)$ by $1$ .

$4 (x + 2) \cdot (- 1)$

Step 3

Apply the distributive property.

$(4 x + 4 \cdot 2) \cdot - 1$

Step 4

Multiply $4$ by $2$ .

$(4 x + 8) \cdot - 1$

Step 5

Apply the distributive property.

$4 x \cdot - 1 + 8 \cdot - 1$

Step 6

Multiply $- 1$ by $4$ .

$- 4 x + 8 \cdot - 1$

Step 7

Multiply $8$ by $- 1$ .

$- 4 x - 8$