Question

Factorize:

$a^2+ab+b^2$

Answer 1

Now,

$a^2+ab+b^2$

$=a^2+(-\omega -{\omega }^2)ab+b^2{\omega }^3$ [ Since $1+\omega +{\omega }^2=0$ and ${\omega }^3=1$]

$=(a-b\omega )(a-b{\omega }^2)$.