Final answer:
The expression 14cd - 28c² - d is factored by first grouping terms and then factoring out common factors to obtain (14c - 1)(d - 4c).
Step-by-step explanation:
To factor the expression 14cd - 28c2 - d, we look for common factors in each term. Observing that the number 7, the variable c, and the variable d appear in some of the terms, we can factor by grouping. The given expression can be grouped as follows: (14cd - d) - 28c2.
To further simplify, we pull out the common factor of d from the first group, resulting in d(14c - 1). There is no common factor for the second group. Now our expression is d(14c - 1) - 28c2. We notice that the term (14c - 1) can be used to factor by grouping across both terms if we factor out a negative sign from the second term, so we get:
d(14c - 1) - 4×7c(7c)
Next, we factor out the common term (14c - 1):
(14c - 1)(d - 4c)
This is the fully factored form of the expression