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

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Answer 1 · 2015-05-03T12:43:42

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)#