Algebra Examples

$x^{2} (x^{2} - 1) - 9 (x^{2} - 1)$

Step 1

Factor $x^{2} - 1$ out of $x^{2} (x^{2} - 1) - 9 (x^{2} - 1)$ .

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Step 1.1

Factor $x^{2} - 1$ out of $x^{2} (x^{2} - 1)$ .

$(x^{2} - 1) x^{2} - 9 (x^{2} - 1)$

Step 1.2

Factor $x^{2} - 1$ out of $- 9 (x^{2} - 1)$ .

$(x^{2} - 1) x^{2} + (x^{2} - 1) \cdot - 9$

Step 1.3

Factor $x^{2} - 1$ out of $(x^{2} - 1) x^{2} + (x^{2} - 1) \cdot - 9$ .

$(x^{2} - 1) (x^{2} - 9)$

Step 2

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

$(x^{2} - 1^{2}) (x^{2} - 9)$

Step 3

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

$(x + 1) (x - 1) (x^{2} - 9)$

Step 4

Rewrite $9$ as $3^{2}$ .

$(x + 1) (x - 1) (x^{2} - 3^{2})$

Step 5

Factor.

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Step 5.1

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 $b = 3$ .

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

Step 5.2

Remove unnecessary parentheses.

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