Algebra Examples

$f (x) = - {(x + 3)}^{2} + 16$

Step 1

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

$f (x) = - {(x + 3)}^{2} + 4^{2}$

Step 2

Reorder $- {(x + 3)}^{2}$ and $4^{2}$ .

$f (x) = 4^{2} - {(x + 3)}^{2}$

Step 3

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 $b = x + 3$ .

$f (x) = (4 + x + 3) (4 - (x + 3))$

Step 4

Simplify.

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Step 4.1

Add $4$ and $3$ .

$f (x) = (x + 7) (4 - (x + 3))$

Step 4.2

Apply the distributive property.

$f (x) = (x + 7) (4 - x - 1 \cdot 3)$

Step 4.3

Multiply $- 1$ by $3$ .

$f (x) = (x + 7) (4 - x - 3)$

Step 4.4

Subtract $3$ from $4$ .

$f (x) = (x + 7) (- x + 1)$