Finite Math Examples

$(x^{2} - 9) (x^{2} - 25)$

Step 1

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

$(x^{2} - 3^{2}) (x^{2} - 25)$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 3$ .

$(x + 3) (x - 3) (x^{2} - 25)$

Step 3

Rewrite $25$ as $5^{2}$ .

$(x + 3) (x - 3) (x^{2} - 5^{2})$

Step 4

Factor.

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Step 4.1

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 $b = 5$ .

$(x + 3) (x - 3) ((x + 5) (x - 5))$

Step 4.2

Remove unnecessary parentheses.

$(x + 3) (x - 3) (x + 5) (x - 5)$