Question 979043
One of the "special products" you were taught about,
along with {{{A^2-B^2=(A-B)(A+B)}}} , is
{{{A^3+B^3=(A+B)(A^2-AB+B^2)}}} ,
and that is the same as {{{a^6+b^6=(a^2)^2+(b^2)^2}}} ,
with {{{system(A=a^2,B=b^2)}}} .
So, {{{highlight(a^6+b^6=(a^2+b^2)(a^4-a^2b^2+b^4))}}} .
That is the "full factorization" ,
because {{{a^2+b^2}}} cannot be factorized,
and neither can {{{a^4-a^2b^2+b^4}}} .