Precalculus Examples

$x^{4} - 625$

Step 1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

${(x^{2})}^{2} - 625$

Step 2

Rewrite $625$ as $25^{2}$ .

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

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x^{2}$ and $b = 25$ .

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

Step 4

Simplify.

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Step 4.1

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

$(x^{2} + 25) (x^{2} - 5^{2})$

Step 4.2

Factor.

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Step 4.2.1

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 $b = 5$ .

$(x^{2} + 25) ((x + 5) (x - 5))$

Step 4.2.2

Remove unnecessary parentheses.

$(x^{2} + 25) (x + 5) (x - 5)$