Factor m^8-n^8

$m^{8} - n^{8}$

Step 1

Rewrite $m^{8}$ as ${(m^{4})}^{2}$ .

${(m^{4})}^{2} - n^{8}$

Step 2

Rewrite $n^{8}$ as ${(n^{4})}^{2}$ .

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

Step 3

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

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

Step 4

Simplify.

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

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

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

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

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 $b = n^{2}$ .

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

Factor.

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

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor m^8-n^8

Related Questions

Support LCMGCF.com by disabling your adblocker.