Algebra Examples

$\frac{x^{2}}{100} - \frac{y^{2} z^{4}}{81}$

Step 1

Rewrite $100$ as $10^{2}$ .

$\frac{x^{2}}{10^{2}} - \frac{y^{2} z^{4}}{81}$

Step 2

Rewrite $\frac{x^{2}}{10^{2}}$ as ${(\frac{x}{10})}^{2}$ .

${(\frac{x}{10})}^{2} - \frac{y^{2} z^{4}}{81}$

Step 3

Rewrite $\frac{y^{2} z^{4}}{81}$ as ${(\frac{y z^{2}}{9})}^{2}$ .

${(\frac{x}{10})}^{2} - {(\frac{y z^{2}}{9})}^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{x}{10}$ and $b = \frac{y z^{2}}{9}$ .

$(\frac{x}{10} + \frac{y z^{2}}{9}) (\frac{x}{10} - \frac{y z^{2}}{9})$