Regular Expression Simplification

Question

Hi my question about Theory of Computation is:

Let $M$ be defined as follows $$M = (K; E; s; D; F )$$ for $$ \begin{align*} K &= \{q_0, q_1, q_2, q_3\}, \\ E &= \{a, b, c\}, \\ s &= q_0, \\ D &= \{(q_0, abc, q_0), (q_0, a, q_1), (q_0, \epsilon, q_3), (q_1, bc, q_1), (q_1, b, q_2), (q_2, a, q_2), (q_2, b, q_3), (q_3, a, q_3)\}, \\ F &= \{q_0, q_2, q_3\}. \end{align*} $$ Find the regular expression describing $L(M)$. Simplify it as much as you can. Explain your steps.

This is what I found for the regular expression: $$\epsilon + (abc)* + (abc)* a (bc)* ba* + (abc)*a(bc)*ba*b + (abc)*a(bc)*ba*ba* + a*.$$

How does that simplify into this: $$(abc)* a(bc)* + \epsilon + a*ba*?$$