Precalculus Examples

$16 - {(x + 2)}^{2}$

Step 1

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

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

Step 2

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

$(4 + x + 2) (4 - (x + 2))$

Step 3

Simplify.

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Step 3.1

Add $4$ and $2$ .

$(x + 6) (4 - (x + 2))$

Step 3.2

Apply the distributive property.

$(x + 6) (4 - x - 1 \cdot 2)$

Step 3.3

Multiply $- 1$ by $2$ .

$(x + 6) (4 - x - 2)$

Step 3.4

Subtract $2$ from $4$ .

$(x + 6) (- x + 2)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- x + 2$ .

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Step 4.1.1

Factor $- 1$ out of $- x$ .

$(x + 6) (- (x) + 2)$

Step 4.1.2

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

$(x + 6) (- (x) - 1 (- 2))$

Step 4.1.3

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

$(x + 6) (- (x - 2))$

Step 4.2

Remove unnecessary parentheses.

$(x + 6) \cdot - 1 (x - 2)$

Step 5

Factor out negative.

$- ((x + 6) (x - 2))$

Step 6

Remove unnecessary parentheses.

$- (x + 6) (x - 2)$