Sure, let's simplify the given expression step by step.
We start with the expression:
[tex]\[ 2b^2(3b^2 + b - 17) \][/tex]
### Step 1: Distribute \( 2b^2 \) through the expression inside the parentheses.
First, multiply \( 2b^2 \) by each term inside the parentheses individually:
1. \( 2b^2 \cdot 3b^2 \):
[tex]\[
= 6b^4
\][/tex]
2. \( 2b^2 \cdot b \):
[tex]\[
= 2b^3
\][/tex]
3. \( 2b^2 \cdot (-17) \):
[tex]\[
= -34b^2
\][/tex]
### Step 2: Combine the results.
After multiplying, we combine all the terms together:
[tex]\[6b^4 + 2b^3 - 34b^2\][/tex]
### Step 3: Identify the coefficients and other requested details.
From our simplified expression \( 6b^4 + 2b^3 - 34b^2 \), we can see:
1. The power of the highest degree term (\(b\)) is \(4\). Therefore, \( 6b^{[4]} \).
2. The coefficient of the \(b^3\) term is \(2\).
3. Notice that there is no \(b\) term in the simplified expression, so its coefficient is \(0\).
### Conclusion:
The simplified form of the expression is:
[tex]\[ 6b^4 + 2b^3 - 34b^2 \][/tex]
In the expression given in the question:
[tex]\[ 6b^{[4]} + \square b^3 - \square b \][/tex]
It translates to:
[tex]\[ 6b^{[4]} + 2b^3 - 0b \][/tex]
Thus:
[tex]\[ 6b^{[4]} + 2b^3 - 0b \][/tex]
