Factor 80z^8-45z^6

$80 z^{8} - 45 z^{6}$

Step 1

Factor $5 z^{6}$ out of $80 z^{8} - 45 z^{6}$ .

Factor $5 z^{6}$ out of $80 z^{8}$ .

$5 z^{6} (16 z^{2}) - 45 z^{6}$

Factor $5 z^{6}$ out of $- 45 z^{6}$ .

$5 z^{6} (16 z^{2}) + 5 z^{6} (- 9)$

Factor $5 z^{6}$ out of $5 z^{6} (16 z^{2}) + 5 z^{6} (- 9)$ .

$5 z^{6} (16 z^{2} - 9)$

Step 2

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

$5 z^{6} ({(4 z)}^{2} - 9)$

Step 3

Rewrite $9$ as $3^{2}$ .

$5 z^{6} ({(4 z)}^{2} - 3^{2})$

Step 4

Factor.

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 z$ and $b = 3$ .

$5 z^{6} ((4 z + 3) (4 z - 3))$

Remove unnecessary parentheses.

$5 z^{6} (4 z + 3) (4 z - 3)$