Please explain how each is expanded and if I even have the right answers:

The function F $=$ CD$$E $+$ CDE $+$ A$$D$$E $+$ A$$B$$DE$+$ BCD is to be implemented in an FPGA which uses $3-$variable lookup tables.

$($a$)$ Expand F about the variables A and B$.$

F $=$ AB$($C$$DE$)+$A$$B$($C$$DE$+$C$$D$)+$AB$($D$$E$+$C$+$C$$D$)+$A$$B$($D$$E$+$C$$DE$)$

$($b$)$ Expand F about the variables B and C$.$

F $=$ BC$($D$)+$B$$C$($D$$E$+$A$)+$BC$($DE$+$A$$D$)+$B$$C$($D$$E$+$DE$)$

$($c$)$ Expand F about the variables A and C$.$

F $=$ AC$($B$$D$$E$+$B$)+$A$$C$($B$$D$$E$)+$AC$($B$$D$$E$+$DE$)+$A$$C$($B$$D$$E$+$DE$+$BD$)$

$($d$)$ Use your preceding answers to implement F using only three $3-$variable lookup tables and a $4-$to$-1$ MUX. Give the truth tables for the lookup tables. Attach files of your circuit implementation and your truth table.