Algebra Examples

$a^{4} - 625$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Simplify.

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Step 4.1

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

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

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 $a = a$ and $b = 5$ .

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

Step 4.2.2

Remove unnecessary parentheses.

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