To determine whether the two expressions are equivalent, let's simplify Expression #1 and see if it matches Expression #2.
**Expression #1:**
\[
(3b + 1) + 10b + 9(3b + 1) + 10b + 9
\]
We can start by distributing \(9\) into \((3b + 1)\):
\[
= (3b + 1) + 10b + (27b + 9) + 10b + 9
\]
Now, combine like terms:
1. Combine the \(b\) terms:
- \(3b + 10b + 27b + 10b\)
- This equals \(3b + 10b + 27b + 10b = 50b\)
2. Combine the constant terms:
- \(1 + 9 + 9\)
- This equals \(1 + 9 + 9 = 19\)
Putting it all together, we have:
\[
Expression #1 = 50b + 19
\]
**Expression #2:**
\[
13b + 9
\]
Now, we need to compare the simplified Expression #1 with Expression #2:
- Expression #1: \(50b + 19\)
- Expression #2: \(13b + 9\)
Clearly, \(50b + 19\) is not equal to \(13b + 9\).
Thus, the two expressions are **not equivalent**.
The final response is:
**The expressions are NOT equivalent.**