Answer :
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].
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].