Algebra Examples

$\frac{x^{2}}{49} - 64$

Step 1

Rewrite $49$ as $7^{2}$ .

$\frac{x^{2}}{7^{2}} - 64$

Step 2

Rewrite $\frac{x^{2}}{7^{2}}$ as ${(\frac{x}{7})}^{2}$ .

${(\frac{x}{7})}^{2} - 64$

Step 3

Rewrite $64$ as $8^{2}$ .

${(\frac{x}{7})}^{2} - 8^{2}$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{x}{7}$ and $b = 8$ .

$(\frac{x}{7} + 8) (\frac{x}{7} - 8)$