Factor a^4z^2-c^6z^4

$a^{4} z^{2} - c^{6} z^{4}$

Step 1

Factor $z^{2}$ out of $a^{4} z^{2} - c^{6} z^{4}$ .

Factor $z^{2}$ out of $a^{4} z^{2}$ .

$z^{2} a^{4} - c^{6} z^{4}$

Factor $z^{2}$ out of $- c^{6} z^{4}$ .

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

Factor $z^{2}$ out of $z^{2} a^{4} + z^{2} (- c^{6} z^{2})$ .

$z^{2} (a^{4} - c^{6} z^{2})$

Step 2

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

$z^{2} ({(a^{2})}^{2} - c^{6} z^{2})$

Step 3

Rewrite $c^{6} z^{2}$ as ${(c^{3} z)}^{2}$ .

$z^{2} ({(a^{2})}^{2} - {(c^{3} z)}^{2})$

Step 4

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

$z^{2} ((a^{2} + c^{3} z) (a^{2} - (c^{3} z)))$

Step 5

Factor.

Remove parentheses.

$z^{2} ((a^{2} + c^{3} z) (a^{2} - c^{3} z))$

Remove unnecessary parentheses.

$z^{2} (a^{2} + c^{3} z) (a^{2} - c^{3} z)$

Factor a^4z^2-c^6z^4

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