To identify which description best fits the expression [tex]\( 4(y + 6) \)[/tex]:
1. First, recognize the structure of the given expression [tex]\( 4(y + 6) \)[/tex].
2. Notice that [tex]\( y + 6 \)[/tex] is a sum of two terms: [tex]\( y \)[/tex] and [tex]\( 6 \)[/tex].
3. Observe that the expression [tex]\( 4(y + 6) \)[/tex] involves multiplying this sum by a constant factor, which is [tex]\( 4 \)[/tex].
Let's analyze each option:
- Option (a): Describes the expression as "the product of a constant factor of four and a factor with the sum of two terms."
- [tex]\( 4 \)[/tex] is a constant factor.
- [tex]\( y + 6 \)[/tex] is the sum of two terms.
- Therefore, [tex]\( 4(y + 6) \)[/tex] correctly fits the description as the product of a constant factor [tex]\( 4 \)[/tex] and a factor [tex]\( y + 6 \)[/tex], which is the sum of two terms.
- Option (b): Describes the expression as "the sum of a constant factor of six and a factor with the product of two terms."
- This is incorrect because the expression is not simply adding six to a product of two terms.
- Option (c): Describes the expression as "the product of two constant factors four and six plus a variable."
- This is incorrect because it suggests [tex]\( 4 \times 6 + y \)[/tex], not [tex]\( 4(y + 6) \)[/tex].
- Option (d): Describes the expression as "the sum of two constant factors four and six plus a variable."
- This is incorrect because it suggests [tex]\( 4 + 6 + y \)[/tex], not [tex]\( 4(y + 6) \)[/tex].
Therefore, the best description that matches the expression [tex]\( 4(y + 6) \)[/tex] is:
(a) The product of a constant factor of four and a factor with the sum of two terms.
