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How do you factor: #y= x^6 - 16x^3 +64x #?

1 Answer

A. S. Adikesavan

Apr 20, 2016

#y=(x-2)^2(x+1+isqrt 3))^2(x+1-isqrt3))^2#

Explanation:

y is a quadratic that is perfect square.

Factorizing this quadratic and using #(a^3-b^3)=(a-b)(a^2+ab+b^2)#,

#y=(x^3-2^3)^2=((x-2)(x^2+2x+4))^2#

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

#=(x-2)^2(x+1+isqrt 3))^2(x+1-isqrt3))^2#

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