X^6 - 3x^4 +3x^2 -1 ? How to factor this easy?

I can not use x^3 = A

1 Answer
MattyMatty
May 26, 2018

#= (x - 1)^3 (x + 1)^3#

Explanation:

#"Use "y = x^2#

#=> y^3 - 3 y^2 + 3 y - 1 = 0#

#"We recognize the binomial coefficients 1 3 3 1 from "(1+x)^3#

#=> (y - 1)^3 = 0#

#=> (x^2 - 1)^3 = ((x - 1)(x + 1))^3 = (x - 1)^3 (x + 1)^3#

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