$$a^4-b^4=(a-b)(a+b)(a^2+b^2)$$
$$\begin{aligned}(a-1)^4 =&a^4-4a^3\cdot1+6a^2\cdot1^2-4a\cdot1^3+1^4\\[1.2em] =&a^4-4a^3-4a+1\end{aligned}$$