Factor each of the following expressions to obtain a product of sums. $($The answer to $($f$)$ should be the product of four terms, each a sum of three variables.$)$

$($a$)AB+C^{\text{'}}{D}^{\text{'}}$

$($b$)Wx+W{Y}^{\text{'}}x+ZYx$

$($c$)A^{\text{'}}BC+EF+DE{F}^{\text{'}}$

$($d$)xYZ+W^{\text{'}}Z+x{Q}^{\text{'}}Z$

$(A+B+D)(A+C+D)(A+B+E)(A+C+E)$

$($e$)AC{D}^{\text{'}}+C^{\text{'}}{D}^{\text{'}}+A^{\text{'}}C$

$($f$)A+BC+DE$

$(A+B+D)(A+C+D)(A+B+E)(A+C+E)$