Evaluate the expression for the given value of the variable. | − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 ; b = − 2
To evaluate the expression, we substitute b = -2 into each term and perform the calculations.
| -4b - 8 | + || -1 - b^2 || + 2b^3
| -4(-2) - 8 | + || -1 - (-2)^2 || + 2(-2)^3
| 8 - 8 | + || -1 - 4 || + 2(-8)
| 0 | + || -1 - 4 || - 16
0 + 5 - 16
= -11
Therefore, the value of the expression when b = -2 is -11.
To evaluate the expression | − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 with b = -2, substitute -2 for b in the expression and simplify each part step-by-step.
Step 1:
Substitute -2 for b in the expression:
| − 4 (-2) − 8 | + ∣ ∣ − 1 − (-2) 2 ∣ ∣ + 2 (-2) 3
Simplify the expression inside absolute value signs (| |):
| 8 − 8 | + ∣ ∣ − 1 − 4 ∣ ∣ + 2 (-8)
Step 2:
Simplify the expression inside absolute value signs (| |):
| 0 | + ∣ ∣ − 1 − 4 ∣ ∣ + 2 (-8)
Since the absolute value of 0 is 0:
0 + ∣ ∣ − 1 − 4 ∣ ∣ + 2 (-8)
Step 3:
Simplify the expression inside absolute value signs (| |):
0 + ∣ 3 ∣ + 2 (-8)
The absolute value of 3 is 3:
0 + 3 + 2 (-8)
Step 4:
Multiply 2 by -8:
0 + 3 - 16
Step 5:
Add 0 and 3, then subtract 16:
3 - 16
Step 6:
Subtract 16 from 3:
-13
Therefore, the value of the expression | − 4 b − 8 | + ∣ ∣ − 1 − b 2 ∣ ∣ + 2 b 3 with b = -2 is -13.
To evaluate the expression | −4b − 8 | + ∣ ∣ −1 − b^2 ∣ ∣ + 2b^3 with b = -2, we will substitute -2 for b and perform the necessary operations step by step.
Step 1: Evaluate the absolute value of −4b − 8:
| −4b − 8 | = |-4(-2) - 8|
= |-8 + 8|
= |0|
= 0
Step 2: Evaluate the absolute value of −1 − b^2:
∣ ∣ −1 − b^2 ∣ ∣ = ∣ ∣ −1 − (-2)^2 ∣ ∣
= ∣ ∣ −1 − 4 ∣ ∣
= ∣ ∣ -5 ∣ ∣
= 5
Step 3: Evaluate the expression 2b^3:
2b^3 = 2(-2)^3
= 2(-8)
= -16
Step 4: Add the results of Step 1, Step 2, and Step 3:
0 + 5 + (-16) = -11
Therefore, when b = -2, the value of the expression | −4b − 8 | + ∣ ∣ −1 − b^2 ∣ ∣ + 2b^3 is -11.