Final answer:
DeMorgan's Theorems are not directly applicable to the given algebraic expression of a sum times a product. The expression simplifies to ABCD after distributive multiplication, as DeMorgan's Theorems relate to Boolean algebra and are not necessary for this algebraic simplification.
Step-by-step explanation:
To apply DeMorgan's Theorems to the given expression ((A + B + C + D)(ABCD)), we need to understand that DeMorgan's Theorems are typically applied to complement operations in Boolean algebra, such as converting the complement of a union to the intersection of complements, and vice versa. However, in the provided expression, we do not have a Boolean complement. Instead, we have a product of a sum and a product of variables.
In this context, DeMorgan's Theorems are not directly applicable, and the expression simplifies using basic algebraic properties. The product of the sum (A + B + C + D) and the product (ABCD) can be distributed as follows: A(ABCD) + B(ABCD) + C(ABCD) + D(ABCD). This expression simplifies further since, for instance, the term A(ABCD) simplifies to ABCD as A multiplied by A is A. The same applies to other terms, leading to the expression ABCD being repeated four times, which does not change its value. Therefore, the simplified expression is simply ABCD.