To determine which option best describes the expression [tex]\(6(y + 3)\)[/tex], let's break down and analyze the expression step by step.
1. Expression Analysis:
- The expression given is [tex]\(6(y + 3)\)[/tex].
- Notice that this expression consists of two main components: the number 6 and the term inside the parentheses, [tex]\(y + 3\)[/tex].
2. Components Description:
- The number 6 is a constant factor. Constants are numbers that do not change.
- The term [tex]\(y + 3\)[/tex] is the sum of two parts:
- The variable [tex]\(y\)[/tex], which can take different values.
- The constant 3, which is a fixed number.
3. Combining the Components:
- The expression [tex]\(6(y + 3)\)[/tex] means that the constant 6 is multiplied by the sum of [tex]\(y\)[/tex] and 3. In other words, 6 is a factor that multiplies the entire quantity inside the parentheses.
4. Choosing the Description:
- Let's examine each choice given to see which one matches our analysis:
- Option 1: "The product of two constant factors six and three plus a variable"
- This is incorrect because it implies there are two constants (six and three) being multiplied, which is not the case here.
- Option 2: "The sum of two constant factors six and three plus a variable"
- This is incorrect because it suggests adding constants six and three, which again does not correctly describe [tex]\(6(y + 3)\)[/tex].
- Option 3: "The product of a constant factor of six and a factor with the sum of two terms"
- This is correct because it correctly describes the expression as the product of the constant 6 and the factor [tex]\(y + 3\)[/tex], which is a sum of two terms [tex]\(y\)[/tex] and 3.
- Option 4: "The sum of a constant factor of three and a factor with the product of two terms"
- This is incorrect because it misinterprets the structure of the expression [tex]\(6(y + 3)\)[/tex].
Therefore, the best description of the expression [tex]\(6(y + 3)\)[/tex] is:
The product of a constant factor of six and a factor with the sum of two terms.
