Factor m^6n-m^2n^5

$m^{6} n - m^{2} n^{5}$

Step 1

Factor $m^{2} n$ out of $m^{6} n - m^{2} n^{5}$ .

Factor $m^{2} n$ out of $m^{6} n$ .

$m^{2} n (m^{4}) - m^{2} n^{5}$

Factor $m^{2} n$ out of $- m^{2} n^{5}$ .

$m^{2} n (m^{4}) + m^{2} n (- 1 n^{4})$

Factor $m^{2} n$ out of $m^{2} n (m^{4}) + m^{2} n (- 1 n^{4})$ .

$m^{2} n (m^{4} - 1 n^{4})$

Step 2

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

$m^{2} n ({(m^{2})}^{2} - 1 n^{4})$

Step 3

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

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

Step 4

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

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

Step 5

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 $b = n$ .

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

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

Factor m^6n-m^2n^5

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