Let's simplify the given expression [tex]\(8y + y + y + 10\)[/tex]:
1. Combine like terms:
- [tex]\(8y + y + y\)[/tex] are terms with [tex]\(y\)[/tex].
- Combine them: [tex]\(8y + y + y = 10y\)[/tex].
2. So, the expression simplifies to:
[tex]\[
10y + 10
\][/tex]
Now we need to check which of the given choices are equivalent to [tex]\(10y + 10\)[/tex]:
- Option A: [tex]\(y + 1\)[/tex]:
[tex]\[
y + 1 \text{ is not equivalent to } 10y + 10.
\][/tex]
- Option B: [tex]\(10y + 1\)[/tex]:
[tex]\[
10y + 1 \text{ is not equivalent to } 10y + 10.
\][/tex]
- Option C: [tex]\(10y + 10\)[/tex]:
[tex]\[
10y + 10 \text{ is exactly } 10y + 10. \text{ (Equivalent) }
\][/tex]
- Option D: [tex]\(10(y + 1)\)[/tex]:
[tex]\[
\text{Expand } 10(y + 1): 10 \cdot y + 10 \cdot 1 = 10y + 10. \text{ (Equivalent) }
\][/tex]
- Option E: [tex]\(10(y + 10)\)[/tex]:
[tex]\[
\text{Expand } 10(y + 10): 10 \cdot y + 10 \cdot 10 = 10y + 100. \text{ (Not equivalent) }
\][/tex]
Therefore, the expressions equivalent to [tex]\(8y + y + y + 10\)[/tex] are:
Option C: [tex]\(10y + 10\)[/tex]
Option D: [tex]\(10(y + 1)\)[/tex]
So, the correct answer is choices [tex]\(C\)[/tex] and [tex]\(D\)[/tex] respectively.
