Factor p^3r^5-p^3r

$p^{3} r^{5} - p^{3} r$

Step 1

Factor $p^{3} r$ out of $p^{3} r^{5} - p^{3} r$ .

Factor $p^{3} r$ out of $p^{3} r^{5}$ .

$p^{3} r (r^{4}) - p^{3} r$

Factor $p^{3} r$ out of $- p^{3} r$ .

$p^{3} r (r^{4}) + p^{3} r (- 1)$

Factor $p^{3} r$ out of $p^{3} r (r^{4}) + p^{3} r (- 1)$ .

$p^{3} r (r^{4} - 1)$

Step 2

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

$p^{3} r ({(r^{2})}^{2} - 1)$

Step 3

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

$p^{3} r ({(r^{2})}^{2} - 1^{2})$

Step 4

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

$p^{3} r ((r^{2} + 1) (r^{2} - 1))$

Step 5

Factor.

Simplify.

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

$p^{3} r ((r^{2} + 1) (r^{2} - 1^{2}))$

Factor.

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

$p^{3} r ((r^{2} + 1) ((r + 1) (r - 1)))$

Remove unnecessary parentheses.

$p^{3} r ((r^{2} + 1) (r + 1) (r - 1))$

Remove unnecessary parentheses.

$p^{3} r (r^{2} + 1) (r + 1) (r - 1)$

Factor p^3r^5-p^3r

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