Basic Math Examples

$\frac{a^{2}}{16} - \frac{b^{2}}{25}$

Step 1

Rewrite $16$ as $4^{2}$ .

$\frac{a^{2}}{4^{2}} - \frac{b^{2}}{25}$

Step 2

Rewrite $\frac{a^{2}}{4^{2}}$ as ${(\frac{a}{4})}^{2}$ .

${(\frac{a}{4})}^{2} - \frac{b^{2}}{25}$

Step 3

Rewrite $\frac{b^{2}}{25}$ as ${(\frac{b}{5})}^{2}$ .

${(\frac{a}{4})}^{2} - {(\frac{b}{5})}^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{a}{4}$ and $b = \frac{b}{5}$ .

$(\frac{a}{4} + \frac{b}{5}) (\frac{a}{4} - \frac{b}{5})$