A regular expression for the language over the alphabet $\{$a$,$ b$\}$ with each string having

an even number of b$$s is $($a$*$ba$*$ba$*)*$a$*.$ Use this result to find regular expressions for

the following languages

a$.$ a language over the same alphabet with each string having $4$n $($n$>=0)$ b$$s$.(4$

points$)$

b$.$ a language over the same alphabet with each string having $4$n$+1($n $>=0)$ b$$s$.$

$(4$ points$)$