Question

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Evaluate the expression for the given value of the variable.

|−4b−8|+|−1−b2|+2b3 ; b=−3

Answer 1

[AI-generated answer — Bot GPT 3.5]

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

Answer 2

[AI-generated answer — Step-by-Step Bot]

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.