Question #a92bd

1 Answer
Cesareo R.
Mar 17, 2017

#x^12-y^12#

Explanation:

#(x-y)(x+y)(x^2+y^2)(x^2+xy+y^2)(x^2-xy+y^2)(x^4-x^2y^2+y^4)#

#(x^2+x y + y^2)=(x^3-y^3)/(x-y)#
#(x^2-x y + y^2)=(x^3+y^3)/(x+y)#
#(x^4-x^2y^2+y^4)=(x^6+y^6)/(x^2+y^2)#

joining all that

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

#=(x-y)(x+y)(x^2+y^2)(x^3-y^3)/(x-y)(x^3+y^3)/(x+y)(x^6+y^6)/(x^2+y^2)=#

#=(x^3-y^3)(x^3+y^3)(x^6+y^6) = x^12-y^12#

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