Precalculus Examples

$4 - {(a + 2)}^{2}$

Step 1

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

$2^{2} - {(a + 2)}^{2}$

Step 2

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

$(2 + a + 2) (2 - (a + 2))$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Add $2$ and $2$ .

$(a + 4) (2 - (a + 2))$

Step 3.2

Apply the distributive property.

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

Step 3.3

Multiply $- 1$ by $2$ .

$(a + 4) (2 - a - 2)$

Step 3.4

Subtract $2$ from $2$ .

$(a + 4) (- a + 0)$

Step 3.5

Factor.

Tap for more steps...

Step 3.5.1

Add $- a$ and $0$ .

$(a + 4) (- a)$

Step 3.5.2

Remove unnecessary parentheses.

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

Step 3.6

Factor out negative.

$- ((a + 4) a)$

Step 4

Remove unnecessary parentheses.

$- (a + 4) a$