Of course, I'd be happy to walk you through the detailed, step-by-step solution for the given expression [tex]\( 2b^3 + 5 \)[/tex] when [tex]\( b = 3 \)[/tex].
### Step 1: Substitution
First, we substitute [tex]\( b \)[/tex] with 3 in the expression [tex]\( 2b^3 + 5 \)[/tex].
[tex]\[ 2b^3 + 5 \rightarrow 2(3)^3 + 5 \][/tex]
### Step 2: Evaluate the Cubic Term
Next, calculate [tex]\( 3^3 \)[/tex] (3 raised to the power of 3).
[tex]\[ 3^3 = 3 \times 3 \times 3 = 27 \][/tex]
### Step 3: Simplify the Expression
Now, substitute [tex]\( 27 \)[/tex] back into the expression.
[tex]\[ 2(3)^3 + 5 \rightarrow 2(27) + 5 \][/tex]
### Step 4: Multiply by 2
Proceed by multiplying [tex]\( 27 \)[/tex] by 2.
[tex]\[ 2 \times 27 = 54 \][/tex]
### Step 5: Add 5
Finally, add 5 to the result obtained from the previous step.
[tex]\[ 54 + 5 = 59 \][/tex]
So the value of the expression [tex]\( 2b^3 + 5 \)[/tex] when [tex]\( b = 3 \)[/tex] is:
[tex]\[ \boxed{59} \][/tex]
