Question

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

Answer 1

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 = (a+b)(a-b)`

`x^4n -81`

`=(sqrt(n)x^2)^2 - 9^2`

`=(sqrt(n)x^2 +9)(sqrt(n)x^2-9)`

`=(sqrt(n)x^2+9)(root(4)(n)x+3)(root(4)(n)x-3)`