Let's evaluate the expression [tex]\( 3a^2 - 7b \)[/tex] step-by-step when [tex]\( a = 3 \)[/tex] and [tex]\( b = -8 \)[/tex]:
1. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the expression:
[tex]\[
3a^2 - 7b \quad \Rightarrow \quad 3(3)^2 - 7(-8)
\][/tex]
2. Calculate [tex]\( a^2 \)[/tex]:
[tex]\[
(3)^2 = 9
\][/tex]
3. Multiply by 3:
[tex]\[
3 \times 9 = 27
\][/tex]
4. Multiply [tex]\(-7\)[/tex] by [tex]\( b \)[/tex]:
[tex]\[
-7 \times (-8) = 56
\][/tex]
5. Combine both results:
[tex]\[
27 + 56 = 83
\][/tex]
Therefore, the expression evaluates to 83.
Hence, the correct answer is:
[tex]\[
\boxed{83}
\][/tex]
