Algebra Examples

$\sqrt{- x^{2} + 4}$

Step 1

Factor $- 1$ out of $- x^{2} + 4$ .

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Step 1.1

Factor $- 1$ out of $- x^{2}$ .

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

Step 1.2

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

$\sqrt{- (x^{2}) - 1 (- 4)}$

Step 1.3

Factor $- 1$ out of $- (x^{2}) - 1 (- 4)$ .

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

Step 2

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

$\sqrt{- (x^{2} - 2^{2})}$

Step 3

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

$\sqrt{- (x + 2) (x - 2)}$