Calculus Examples

$1 - 4 x^{- 2}$

Step 1

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

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

Step 2

Rewrite $4 x^{- 2}$ as ${(2 x^{- 1})}^{2}$ .

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

Step 3

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

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4.2

Combine $2$ and $\frac{1}{x}$ .

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

Step 4.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 4.4

Combine $2$ and $\frac{1}{x}$ .

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