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Evaluate the expression for the given value of the variable.
|−4b−8|+|−1−b2|+2b3 ; b=−3
To evaluate the expression, we substitute b = -3 into the expression:
|-4(-3) - 8| + |-1 - (-3)^2| + 2(-3)^3
Simplifying the exponent and multiplication first:
|-12 - 8| + |-1 - 9| + 2(-27)
|-20| + |-10| + -54
Since absolute value is always positive, we can remove the absolute value symbols:
20 + 10 + (-54)
Next, we can add the numbers together:
30 + (-54)
Finally, we can simplify the addition:
= -24
To evaluate this expression for the given value of the variable, b = -3, we substitute -3 for b in the expression.
|-4b - 8| + |-1 - b^2| + 2b^3
Step 1: Substitute b = -3 in the expression.
|-4(-3) - 8| + |-1 - (-3)^2| + 2(-3)^3
Step 2: Simplify the expression inside the absolute value symbols.
|-12 - 8| + |-1 - 9| + 2(-27)
Step 3: Evaluate the absolute values.
| -20 | + | -10 | - 54
Step 4: Simplify the expression inside the absolute value.
20 + 10 - 54
Step 5: Perform the addition and subtraction from left to right.
30 - 54
Step 6: Perform the subtraction.
-24
Therefore, when b = -3, the value of the expression |-4b - 8| + |-1 - b^2| + 2b^3 is -24.