To determine the value of [tex]\( y \)[/tex] when [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex] given the equation [tex]\( y = 3ab + 2b^3 \)[/tex], we will substitute these values into the equation and perform the necessary calculations step-by-step.
1. Substitute [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex] into the equation [tex]\( y = 3ab + 2b^3 \)[/tex]:
[tex]\[
y = 3(1)(2) + 2(2)^3
\][/tex]
2. Calculate the first term [tex]\( 3ab \)[/tex]:
[tex]\[
3ab = 3 \cdot 1 \cdot 2 = 6
\][/tex]
3. Calculate the second term [tex]\( 2b^3 \)[/tex]:
[tex]\[
2b^3 = 2 \cdot (2)^3
\][/tex]
Since [tex]\( (2)^3 = 2 \cdot 2 \cdot 2 = 8 \)[/tex]:
[tex]\[
2b^3 = 2 \cdot 8 = 16
\][/tex]
4. Add the two terms together to find [tex]\( y \)[/tex]:
[tex]\[
y = 6 + 16 = 22
\][/tex]
Therefore, when [tex]\( a = 1 \)[/tex] and [tex]\( b = 2 \)[/tex], the value of [tex]\( y \)[/tex] is [tex]\( 22 \)[/tex].
So, the correct answer is:
[tex]\[
22
\][/tex]
