Certainly! Let's evaluate the expression [tex]\( 4a^3 + 6b^2 - 14 \)[/tex] given [tex]\( a = 2 \)[/tex] and [tex]\( b = -1 \)[/tex].
1. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the expression:
[tex]\[
4(2)^3 + 6(-1)^2 - 14
\][/tex]
2. Calculate [tex]\( (2)^3 \)[/tex]:
[tex]\[
(2)^3 = 2 \times 2 \times 2 = 8
\][/tex]
Substitute this back into the expression:
[tex]\[
4 \times 8 + 6(-1)^2 - 14
\][/tex]
3. Multiply [tex]\( 4 \)[/tex] and [tex]\( 8 \)[/tex]:
[tex]\[
4 \times 8 = 32
\][/tex]
Substitute this result back into the expression:
[tex]\[
32 + 6(-1)^2 - 14
\][/tex]
4. Calculate [tex]\( (-1)^2 \)[/tex]:
[tex]\[
(-1)^2 = (-1) \times (-1) = 1
\][/tex]
Substitute this back into the expression:
[tex]\[
32 + 6 \times 1 - 14
\][/tex]
5. Multiply [tex]\( 6 \)[/tex] and [tex]\( 1 \)[/tex]:
[tex]\[
6 \times 1 = 6
\][/tex]
Substitute this result back into the expression:
[tex]\[
32 + 6 - 14
\][/tex]
6. Combine the terms:
[tex]\[
32 + 6 = 38
\][/tex]
[tex]\[
38 - 14 = 24
\][/tex]
Therefore, the value of the expression [tex]\( 4a^3 + 6b^2 - 14 \)[/tex] when [tex]\( a = 2 \)[/tex] and [tex]\( b = -1 \)[/tex] is [tex]\( 24 \)[/tex].
