Algebra Examples

$(a^{2} - 1) b^{2} - 4 (a^{2} - 1)$

Step 1

Factor $a^{2} - 1$ out of $(a^{2} - 1) b^{2} - 4 (a^{2} - 1)$ .

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Step 1.1

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

$(a^{2} - 1) (b^{2}) - 4 (a^{2} - 1)$

Step 1.2

Factor $a^{2} - 1$ out of $- 4 (a^{2} - 1)$ .

$(a^{2} - 1) (b^{2}) + (a^{2} - 1) \cdot - 4$

Step 1.3

Factor $a^{2} - 1$ out of $(a^{2} - 1) (b^{2}) + (a^{2} - 1) \cdot - 4$ .

$(a^{2} - 1) (b^{2} - 4)$

Step 2

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

$(a^{2} - 1^{2}) (b^{2} - 4)$

Step 3

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

$(a + 1) (a - 1) (b^{2} - 4)$

Step 4

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

$(a + 1) (a - 1) (b^{2} - 2^{2})$

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 $a = b$ and $b = 2$ .

$(a + 1) (a - 1) ((b + 2) (b - 2))$

Step 5.2

Remove unnecessary parentheses.

$(a + 1) (a - 1) (b + 2) (b - 2)$