Clifland

2021-02-15

Factor the polynomial. ${t}^{4}-1$

ottcomn

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