Difference of cubes?

Question

how solve x^6 -64 using difference of cubes.

 

The answer is (x-2)(x+2)(x^4+4x^2+16)

 

thankyou

Answer 1

x^6-64 can be transformed to

(x^2)^3-(2^2)^3 this is difference of cubes and you can factor it to

(x^2-2^2)[(x^2)^2+2^2(x^2)+(2^2)^2]

first factor can be factored as (x-2)(x+2)

second factor can be simplified as

x^4+4x^2+16 so the answer is

(x-2)(x+2)(x^4+4x^2+16)