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Select the expressions that are equivalent to [tex]\( 5(5v + 8) + 8v \)[/tex].

[tex]\[
\begin{array}{c}
A. \ 5(8v + 5) + 8v \\
B. \ 33v + 8 \\
C. \ 8(5v + 5) + 8v \\
D. \ 33v + 40
\end{array}
\][/tex]



Answer :

GinnyAnswer
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].

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