Factor 256n^4-c^4

$256 n^{4} - c^{4}$

Step 1

Rewrite $256 n^{4}$ as ${(16 n^{2})}^{2}$ .

${(16 n^{2})}^{2} - c^{4}$

Step 2

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

${(16 n^{2})}^{2} - {(c^{2})}^{2}$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 16 n^{2}$ and $b = c^{2}$ .

$(16 n^{2} + c^{2}) (16 n^{2} - c^{2})$

Step 4

Simplify.

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

$(16 n^{2} + c^{2}) ({(4 n)}^{2} - c^{2})$

Factor.

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

$(16 n^{2} + c^{2}) ((4 n + c) (4 n - c))$

Remove unnecessary parentheses.

$(16 n^{2} + c^{2}) (4 n + c) (4 n - c)$

Factor 256n^4-c^4

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