Consider the regular expression:

$($a $+$ b$)$a$($a $+$ b$)$b$($a $+$ b$)$

Show that this is equivalent to

$($a $+$ b$)$ab$($a $+$ b$)$

in the sense that they define the same language. $($ii$)$ Show that

$($a$+$b$)$ab$($a$+$b$)+$b$$a$=($a$+$b$)$