Factor by Grouping

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

Step 1

Add $- x$ and $x$ .

$x^{2} + 0 - 1$

Step 2

Add $x^{2}$ and $0$ .

$x^{2} - 1$

Step 3

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

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

Step 4

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

$(x + 1) (x - 1)$

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$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$