Factor 32z^5-2z

$32 z^{5} - 2 z$

Step 1

Factor $2 z$ out of $32 z^{5} - 2 z$ .

Factor $2 z$ out of $32 z^{5}$ .

$2 z (16 z^{4}) - 2 z$

Factor $2 z$ out of $- 2 z$ .

$2 z (16 z^{4}) + 2 z (- 1)$

Factor $2 z$ out of $2 z (16 z^{4}) + 2 z (- 1)$ .

$2 z (16 z^{4} - 1)$

Step 2

Rewrite $16 z^{4}$ as ${(4 z^{2})}^{2}$ .

$2 z ({(4 z^{2})}^{2} - 1)$

Step 3

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

$2 z ({(4 z^{2})}^{2} - 1^{2})$

Step 4

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 z^{2}$ and $b = 1$ .

$2 z ((4 z^{2} + 1) (4 z^{2} - 1))$

Step 5

Factor.

Simplify.

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

$2 z ((4 z^{2} + 1) ({(2 z)}^{2} - 1))$

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

$2 z ((4 z^{2} + 1) ({(2 z)}^{2} - 1^{2}))$

Factor.

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

$2 z ((4 z^{2} + 1) ((2 z + 1) (2 z - 1)))$

Remove unnecessary parentheses.

$2 z ((4 z^{2} + 1) (2 z + 1) (2 z - 1))$

Remove unnecessary parentheses.

$2 z (4 z^{2} + 1) (2 z + 1) (2 z - 1)$

Factor 32z^5-2z

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