a.
a^6-b^6=(a³)²-(b³)²=(a³+b³)(a³-b³)=(a+b)(a²-ab+b²)(a-b)(a²+ab+b²)=
=(a+b)(a-b)(a²-ab+b²)(a²+ab+b²)
b.
a^6+b^6=(a²)³+(b²)³=(a²+b²)(a^4-a²b²+b^4)=(a²+b²)[(a^4+b^4)-a²b²]=
=(a²+b²)[(a²+b²)²-2a²b²-a²b²]=(a²+b²)[(a²+b²)²-3a²b²]=(a²+b²)(a²+b²+√3ab)(a²+b²-√3ab)
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a.
a^6-b^6=(a³)²-(b³)²=(a³+b³)(a³-b³)=(a+b)(a²-ab+b²)(a-b)(a²+ab+b²)=
=(a+b)(a-b)(a²-ab+b²)(a²+ab+b²)
b.
a^6+b^6=(a²)³+(b²)³=(a²+b²)(a^4-a²b²+b^4)=(a²+b²)[(a^4+b^4)-a²b²]=
=(a²+b²)[(a²+b²)²-2a²b²-a²b²]=(a²+b²)[(a²+b²)²-3a²b²]=(a²+b²)(a²+b²+√3ab)(a²+b²-√3ab)