Factor -n^(8x+2y)+m^(6x-4y)

$- n^{8 x + 2 y} + m^{6 x - 4 y}$

Rewrite $m^{6 x - 4 y}$ as ${(m^{3 x - 2 y})}^{2}$ .

$- n^{8 x + 2 y} + {(m^{3 x - 2 y})}^{2}$

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

$- {(n^{4 x + y})}^{2} + {(m^{3 x - 2 y})}^{2}$

Reorder $- {(n^{4 x + y})}^{2}$ and ${(m^{3 x - 2 y})}^{2}$ .

${(m^{3 x - 2 y})}^{2} - {(n^{4 x + y})}^{2}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m^{3 x - 2 y}$ and $b = n^{4 x + y}$ .

$(m^{3 x - 2 y} + n^{4 x + y}) (m^{3 x - 2 y} - n^{4 x + y})$

Factor -n^(8x+2y)+m^(6x-4y)

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