Algebra Examples

$4^{2 x} - 1$

Step 1

Rewrite $4^{2 x}$ as ${(4^{x})}^{2}$ .

${(4^{x})}^{2} - 1$

Step 2

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

${(4^{x})}^{2} - 1^{2}$

Step 3

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

$(4^{x} + 1) (4^{x} - 1)$