Pre-Algebra Examples

$\frac{1}{9} - 16 z^{2}$

Step 1

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

$\frac{1^{2}}{9} - 16 z^{2}$

Step 2

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

$\frac{1^{2}}{3^{2}} - 16 z^{2}$

Step 3

Rewrite $\frac{1^{2}}{3^{2}}$ as ${(\frac{1}{3})}^{2}$ .

${(\frac{1}{3})}^{2} - 16 z^{2}$

Step 4

Rewrite $16 z^{2}$ as ${(4 z)}^{2}$ .

${(\frac{1}{3})}^{2} - {(4 z)}^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{1}{3}$ and $b = 4 z$ .

$(\frac{1}{3} + 4 z) (\frac{1}{3} - (4 z))$

Step 6

Multiply $4$ by $- 1$ .

$(\frac{1}{3} + 4 z) (\frac{1}{3} - 4 z)$