Algebra Examples

$\sqrt{3 - x} \cdot \sqrt{x^{2} - 1}$

Step 1

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

$\sqrt{3 - x} \cdot \sqrt{x^{2} - 1^{2}}$

Step 2

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

$\sqrt{3 - x} \cdot \sqrt{(x + 1) (x - 1)}$

Step 3

Combine using the product rule for radicals.

$\sqrt{(3 - x) (x + 1) (x - 1)}$