Precalculus Examples

$\sqrt{9 - 4 x^{2}}$

Step 1

Write the expression using exponents.

Tap for more steps...

Step 1.1

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} - 4 x^{2}}$

Step 1.2

Rewrite $4 x^{2}$ as ${(2 x)}^{2}$ .

$\sqrt{3^{2} - {(2 x)}^{2}}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 3$ and $b = 2 x$ .

$\sqrt{(3 + 2 x) (3 - (2 x))}$

Step 3

Multiply $2$ by $- 1$ .

$\sqrt{(3 + 2 x) (3 - 2 x)}$