Factor m^4-n^4

$m^{4} - n^{4}$

Step 1

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

${(m^{2})}^{2} - n^{4}$

Step 2

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

${(m^{2})}^{2} - {(n^{2})}^{2}$

Step 3

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

$(m^{2} + n^{2}) (m^{2} - n^{2})$

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 $a = m$ and $b = n$ .

$(m^{2} + n^{2}) ((m + n) (m - n))$

Remove unnecessary parentheses.

$(m^{2} + n^{2}) (m + n) (m - n)$

Factor m^4-n^4

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