Question

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

(a) a'b' a'cd a'df'
(b) g'h' jk
(c) a'bc a'b'c cd'
(d) a'b' (cd' f)
(e) a'b'c b'cd' fg'
(f) wx'y w'x' w'y'

Answer 1

To factor each expression and obtain a product of sums, we need to use the distributive property and combine like terms.

Step-by-step explanation:

To factor each of the given expressions to obtain a product of sums, we need to use the distributive property and combine like terms.

1. (a) a'b' a'cd a'df'
   First, we can group the common terms together: a'b' + a'cd + a'df'
   Next, we can apply the distributive property to factor out the common terms: a'(b' + cd + df')
   This gives us the factored expression: a'(b' + cd + df')
2. (b) g'h' jk
   There are no common terms to factor, so the expression remains as it is: g'h' jk
3. (c) a'bc a'b'c cd'
   First, we can group the common terms together: a'bc + a'b'c + cd'
   Next, we can apply the distributive property to factor out the common terms: a'(bc + b'c) + cd'
   This gives us the factored expression: a'(bc + b'c) + cd'