Basic Math Examples

$6 a^{8} - 6 p^{8}$

Step 1

Factor $6$ out of $6 a^{8} - 6 p^{8}$ .

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Step 1.1

Factor $6$ out of $6 a^{8}$ .

$6 (a^{8}) - 6 p^{8}$

Step 1.2

Factor $6$ out of $- 6 p^{8}$ .

$6 (a^{8}) + 6 (- p^{8})$

Step 1.3

Factor $6$ out of $6 (a^{8}) + 6 (- p^{8})$ .

$6 (a^{8} - p^{8})$

Step 2

Rewrite $a^{8}$ as ${(a^{4})}^{2}$ .

$6 ({(a^{4})}^{2} - p^{8})$

Step 3

Rewrite $p^{8}$ as ${(p^{4})}^{2}$ .

$6 ({(a^{4})}^{2} - {(p^{4})}^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a^{4}$ and $b = p^{4}$ .

$6 ((a^{4} + p^{4}) (a^{4} - p^{4}))$

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

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

$6 ((a^{4} + p^{4}) ({(a^{2})}^{2} - p^{4}))$

Step 5.1.2

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

$6 ((a^{4} + p^{4}) ({(a^{2})}^{2} - {(p^{2})}^{2}))$

Step 5.1.3

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 $b = p^{2}$ .

$6 ((a^{4} + p^{4}) ((a^{2} + p^{2}) (a^{2} - p^{2})))$

Step 5.1.4

Factor.

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Step 5.1.4.1

Factor.

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Step 5.1.4.1.1

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 $b = p$ .

$6 ((a^{4} + p^{4}) ((a^{2} + p^{2}) ((a + p) (a - p))))$

Step 5.1.4.1.2

Remove unnecessary parentheses.

$6 ((a^{4} + p^{4}) ((a^{2} + p^{2}) (a + p) (a - p)))$

Step 5.1.4.2

Remove unnecessary parentheses.

$6 ((a^{4} + p^{4}) (a^{2} + p^{2}) (a + p) (a - p))$

Step 5.2

Remove unnecessary parentheses.

$6 (a^{4} + p^{4}) (a^{2} + p^{2}) (a + p) (a - p)$