Find one factor of the form $a^{k}+m$, where $a^{k}$ divides the monomial with the highest power $a^{6}$ and $m$ divides the constant factor $1$. One such factor is $a^{3}-1$. Factor the polynomial by dividing it by this factor.
$$\left(a^{3}-1\right)\left(a^{3}-1\right)$$
Consider $a^{3}-1$. Rewrite $a^{3}-1$ as $a^{3}-1^{3}$. The difference of cubes can be factored using the rule: $p^{3}-q^{3}=\left(p-q\right)\left(p^{2}+pq+q^{2}\right)$.
$$\left(a-1\right)\left(a^{2}+a+1\right)$$
Rewrite the complete factored expression. Polynomial $a^{2}+a+1$ is not factored since it does not have any rational roots.
