To determine which algebraic expression contains a product with a factor of 5, let's examine each option closely.
Option A: [tex]\(-2y + 5 + 3\)[/tex]
- This expression is a sum of terms: [tex]\(-2y\)[/tex], [tex]\(5\)[/tex], and [tex]\(3\)[/tex].
- There is no multiplication involving 5.
- Therefore, it is not a product with a factor of 5.
Option B: [tex]\(3y + 1\)[/tex]
- This is a sum of terms: [tex]\(3y\)[/tex] and [tex]\(1\)[/tex].
- There is no multiplication involving 5.
- Therefore, it is not a product with a factor of 5.
Option C: [tex]\(5y - 7\)[/tex]
- This expression is a difference of terms: [tex]\(5y\)[/tex] and [tex]\(7\)[/tex].
- Although it contains the term [tex]\(5y\)[/tex], which has a 5 in it, it is not in the form of a product because [tex]\(5y\)[/tex] is itself a term, not a multiplication factor.
- Therefore, it is not considered a product with a factor of 5 by itself.
Option D: [tex]\(5(y - 6)\)[/tex]
- This expression is a product of 5 and the term [tex]\((y - 6)\)[/tex].
- Here, we have a clear multiplication involving the factor 5.
- Therefore, this is a product with a factor of 5.
Based on this detailed analysis, the correct answer is:
D. [tex]\(5(y - 6)\)[/tex]
