Basic Math Examples

$\frac{n^{2014} - 1}{{(n - 1)}^{2}}$

Step 1

Rewrite $n^{2014}$ as ${(n^{1007})}^{2}$ .

$\frac{{(n^{1007})}^{2} - 1}{{(n - 1)}^{2}}$

Step 2

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

$\frac{{(n^{1007})}^{2} - 1^{2}}{{(n - 1)}^{2}}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = n^{1007}$ and $b = 1$ .

$\frac{(n^{1007} + 1) (n^{1007} - 1)}{{(n - 1)}^{2}}$