Let's carefully analyze the given expression [tex]\(2a + 3b + 4c + 5d\)[/tex] and determine which description fits it best.
### Step-by-Step Solution:
1. Identify the Structure:
The given expression is [tex]\(2a + 3b + 4c + 5d\)[/tex]. It is comprised of terms separated by the plus sign (+).
2. Determine the Nature of Each Term:
Each term in the expression is a product of a coefficient with a variable:
- [tex]\(2a\)[/tex] is a product where 2 is the coefficient and [tex]\(a\)[/tex] is the variable.
- [tex]\(3b\)[/tex] is a product where 3 is the coefficient and [tex]\(b\)[/tex] is the variable.
- [tex]\(4c\)[/tex] is a product where 4 is the coefficient and [tex]\(c\)[/tex] is the variable.
- [tex]\(5d\)[/tex] is a product where 5 is the coefficient and [tex]\(d\)[/tex] is the variable.
3. Count the Number of Terms:
The expression has four terms:
- [tex]\(2a\)[/tex]
- [tex]\(3b\)[/tex]
- [tex]\(4c\)[/tex]
- [tex]\(5d\)[/tex]
4. Classify the Entire Expression:
Now, let's classify the expression:
- It is a sum because we are adding up different terms.
- Each term itself is a product of a coefficient and a variable.
Therefore, [tex]\(2a + 3b + 4c + 5d\)[/tex] is recognized as the sum of multiple products, each product being a multiplication of a coefficient and a variable.
5. Determine the Correct Description:
Among the options given:
- a states it as the product of four sums, which implies multiplying sums – this is not accurate.
- b also describes it as the product of sums, with eight terms – still not the case.
- c describes it as the sum of four products with four terms, which fits our analysis perfectly.
- d describes it as the sum of four products with eight terms, which does not fit since there are only four terms.
The best description of [tex]\(2a + 3b + 4c + 5d\)[/tex] is option c: The sum of four products; there are four terms.
Thus, the correct answer is:
c The sum of four products; there are four terms.
