Obviously yes because every single string ends in c*.

Obviously yes because every single string ends in c*.

Note that (x)*y is always a superset of y, so if both are present then y can be removed. We do this and get

$a^*(ac^* + b^*bc^* + b^*cc^* ) + c^*$

$b^*cc^*$ includes $c^*$ except $\epsilon$, so this is $a^* (a + b^*b + b^*c) c^* + \epsilon = a^* (a + b^*(b + c)) c^* + \epsilon $