Certainly! Let's evaluate the expression [tex]\( 2b^3 + 5 \)[/tex] step by step when [tex]\( b = 3 \)[/tex].
1. Substitute the value of [tex]\( b \)[/tex] into the expression:
Given that [tex]\( b = 3 \)[/tex], the expression becomes:
[tex]\[
2(3)^3 + 5
\][/tex]
2. Calculate [tex]\( 3^3 \)[/tex]:
To find [tex]\( 3^3 \)[/tex], we multiply 3 by itself two more times:
[tex]\[
3 \times 3 = 9
\][/tex]
[tex]\[
9 \times 3 = 27
\][/tex]
Therefore,
[tex]\[
3^3 = 27
\][/tex]
3. Multiply [tex]\( 27 \)[/tex] by [tex]\( 2 \)[/tex]:
Now we need to multiply the result of [tex]\( 3^3 \)[/tex] by 2:
[tex]\[
2 \times 27 = 54
\][/tex]
4. Add [tex]\( 5 \)[/tex] to [tex]\( 54 \)[/tex]:
Finally, we add 5 to the result:
[tex]\[
54 + 5 = 59
\][/tex]
So, the value of the expression [tex]\( 2b^3 + 5 \)[/tex] when [tex]\( b = 3 \)[/tex] is [tex]\( 59 \)[/tex].
