To determine which of these expressions are equivalent to [tex]\( 5(5v + 8) + 8v \)[/tex], we need to simplify each expression step by step and compare them with the original expression.
### Step-by-Step Simplification:
1. Simplify the original expression [tex]\( 5(5v + 8) + 8v \)[/tex]:
[tex]\( 5(5v + 8) = 25v + 40 \)[/tex]
[tex]\( 25v + 40 + 8v = 33v + 40 \)[/tex]
So, the simplified form of [tex]\( 5(5v + 8) + 8v \)[/tex] is [tex]\( 33v + 40 \)[/tex].
Now, let’s check each given expression to see if it simplifies to [tex]\( 33v + 40 \)[/tex].
2. Check [tex]\( 5(8v + 5) + 8v \)[/tex]:
[tex]\( 5(8v + 5) = 40v + 25 \)[/tex]
[tex]\( 40v + 25 + 8v = 48v + 25 \)[/tex]
This does not match [tex]\( 33v + 40 \)[/tex].
3. Check [tex]\( 33v + 8 \)[/tex]:
This is already simplified and does not match [tex]\( 33v + 40 \)[/tex].
4. Check [tex]\( 8(5v + 5) + 8v \)[/tex]:
[tex]\( 8(5v + 5) = 40v + 40 \)[/tex]
[tex]\( 40v + 40 + 8v = 48v + 40 \)[/tex]
This does not match [tex]\( 33v + 40 \)[/tex].
5. Check [tex]\( 33v + 40 \)[/tex]:
This is already simplified and it exactly matches [tex]\( 33v + 40 \)[/tex].
### Conclusion:
The expression that is equivalent to [tex]\( 5(5v + 8) + 8v \)[/tex] is:
[tex]\[ 33v + 40 \][/tex]
So, the correct selection is the fourth expression, [tex]\(\boxed{33v + 40}\)[/tex].
