Simplify the following Boolean expressions. Show your work:

a$-($BC$+$BC$\text{'})\text{'}+$AB$+$A

b$-$ A$\text{'}($A$+$B$)+($B$+$AA$)($A$+$B$)$

c$-$ A$($A$+$B$\text{'}$C$)+$A$($B$\text{'}+$C$)$