# How do you use the difference of two squares formula to factor x^4n - 81 ?

May 3, 2015

I have to wonder if the $n$ in your expression is an error; but assuming it isn't:

The general equation for the difference of two squares is
${a}^{2} - {b}^{2} = \left(a + b\right) \left(a - b\right)$

${x}^{4} n - 81$

$= {\left(\sqrt{n} {x}^{2}\right)}^{2} - {9}^{2}$

$= \left(\sqrt{n} {x}^{2} + 9\right) \left(\sqrt{n} {x}^{2} - 9\right)$

$= \left(\sqrt{n} {x}^{2} + 9\right) \left(\sqrt[4]{n} x + 3\right) \left(\sqrt[4]{n} x - 3\right)$