${t}^{4}-1$ As ${t}^{4}=({t}^{2}{)}^{2}$ and $1={1}^{2}$, we have $({t}^{2}{)}^{2}\u2013{1}^{2}=({t}^{2}+1)({t}^{2}\u20131)$, (by the special product rule that states ${a}^{2}\u2013{b}^{2}=(a\u2013b)(a+b))$ And we can factor $({t}^{2}\u20131)\text{}as\text{}(t+1)(t\u20131)$. Then we have $({t}^{2}+1)(t+1)(t\u20131)$.