Algebra Examples

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

Step 1

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

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

Step 2

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

$(x - 1 + 2) (x - 1 - 2)$

Step 3

Simplify.

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Step 3.1

Add $- 1$ and $2$ .

$(x + 1) (x - 1 - 2)$

Step 3.2

Subtract $2$ from $- 1$ .

$(x + 1) (x - 3)$