Precalculus Examples

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

Step 1

Rewrite $1$ as $1^{2}$ .

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x^{2}$ .

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

Step 3

Simplify.

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Step 3.1

Rewrite $1$ as $1^{2}$ .

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

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 1$ and $b = x$ .

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