Question 31: Factorize the polynomial \(\begin{aligned} & a^{8}-1 \end{aligned}\)

\(\begin{aligned} & a^{8}-1 \\ &=\left(a^{4}\right)^{2}-1 \\ &=\left(a^{4}-1 \right)\left(a^{4}+1\right) \\ &=\left(a^{2}-1\right)\left(a^{2}+1\right)\left(a ^{4}+1\right) \\ &=(a-1)(a+1)\left(a^{2}+1\right)\left(a^{4}+1\right) \ end{aligned}\)