I need to derive this equation and get the below result.

$\displaystyle ((a^2-b^2)^2+a^2b^2)(a^2+b^2)=a^6+b^6$

$\displaystyle ===>$ $\displaystyle (a^2-iab-b^2)(a+ib)=a^3-ib^3$

Also a hint teacher gave us:

replace

$\displaystyle a$ by $\displaystyle a^2$

$\displaystyle b$ by $\displaystyle -ib^2$

I tried few things (like $\displaystyle -b^2=-1.b^2=i^2b^2$) to involve complex numbers in the first equation but im confused and have no clue what to do.