Question

Factor each of the following expressions to obtain a product of sums:

(a) AB+CD′
(b) WX+WY′X+ZYX
(c) A′BC+EF+DEF′
(d) XYZ+W′Z+XQ′Z
(e) ACD′+CD′+A′C
(f) A+BC+DE

(The answer to (f) should be the product of four terms, each a sum of three varia

Answer 1

To factor the given expressions into a product of sums, we look for common factors and group them accordingly.

Step-by-step explanation:

To factor each of the given expressions to obtain a product of sums, we need to look for common factors to group them. Let's go through each expression:

(a) AB+CD': There are no common factors, so this is already in factored form.

(b) WX+WY'X+ZYX: We can factor out X from the first two terms to get X(W+BY') + ZYX.

(c) A'BC+EF+DEF': There are no common factors, so this is already in factored form.

(d) XYZ+W'Z+XQ'Z: There are no common factors, so this is already in factored form.

(e) ACD'+CD'+A'C: We can factor out CD' from the first two terms to get CD'(A+1) + A'C.

(f) A+BC+DE: We can factor out A from the first term and B from the second term to get A(1+CB)+DE.