Algebra Examples

$\frac{1}{16} - \frac{4 x^{2}}{49}$

Step 1

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

$\frac{1^{2}}{16} - \frac{4 x^{2}}{49}$

Step 2

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

$\frac{1^{2}}{4^{2}} - \frac{4 x^{2}}{49}$

Step 3

Rewrite $\frac{1^{2}}{4^{2}}$ as ${(\frac{1}{4})}^{2}$ .

${(\frac{1}{4})}^{2} - \frac{4 x^{2}}{49}$

Step 4

Rewrite $\frac{4 x^{2}}{49}$ as ${(\frac{2 x}{7})}^{2}$ .

${(\frac{1}{4})}^{2} - {(\frac{2 x}{7})}^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = \frac{1}{4}$ and $b = \frac{2 x}{7}$ .

$(\frac{1}{4} + \frac{2 x}{7}) (\frac{1}{4} - \frac{2 x}{7})$