Precalculus Examples

$\frac{1}{4} - 9 a^{2}$

Step 1

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

$\frac{1^{2}}{4} - 9 a^{2}$

Step 2

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

$\frac{1^{2}}{2^{2}} - 9 a^{2}$

Step 3

Rewrite $\frac{1^{2}}{2^{2}}$ as ${(\frac{1}{2})}^{2}$ .

${(\frac{1}{2})}^{2} - 9 a^{2}$

Step 4

Rewrite $9 a^{2}$ as ${(3 a)}^{2}$ .

${(\frac{1}{2})}^{2} - {(3 a)}^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{1}{2}$ and $b = 3 a$ .

$(\frac{1}{2} + 3 a) (\frac{1}{2} - (3 a))$

Step 6

Multiply $3$ by $- 1$ .

$(\frac{1}{2} + 3 a) (\frac{1}{2} - 3 a)$