Question

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

Evaluate the expression for the given value of the variable.


4b−8|+∣∣−1 − b^2∣∣+ 2b^3; b=−2


please help

Answer 1

To solve the problem, we substitute -2 for b in each term of the expression, take absolute values where indicated, and then sum the terms to find the value of the expression is 5.

Step-by-step explanation:

To evaluate the expression given the variable b = -2, we substitute b into the expression:

4b - 8 + | -1 -
`b^2`| +
`2b^3`

First, we calculate each term with b = -2:

• 4b - 8 = 4(-2) - 8 = -8 - 8 = -16
• -1 -
  `b^2`= -1 -
  `(-2)^2` = -1 - 4 = -5
• 
  `2b^3`=
  `2(-2)^3` = 2(-8) = -16

Then we take the absolute value of each term where needed:

• |4b - 8| = |-16| = 16
• |-1 - b2| = |-5| = 5
• 2b3 = -16 (no absolute value needed)

Finally, we sum up all the terms:

16 + 5 - 16 = 5

The value of the expression when b = -2 is 5.

Answer 2

Question: Evaluate the expression for the given value of the variable. | − 4b − 8 | + ∣ − 1 − b² | + 2b³; b = − 2

Answer:

-11

Step-by-step explanation:

What we are required to do here is to find the value of the expression assuming that variable b = -2.

Bear in mind that, where you see the symbol "| ... |", enclosing a set of terms, the absolute value after performing whatever function with the enclosed terms is what is to be found. This means, after performing the operation, if you have a negative value, simply ignore the negative sign.

Now let's evaluate at b = -2

|- 4b - 8| + ∣-1 - b²| + 2b³ (given)

|- 4(-2) - 8| + ∣-1 - (-2)²| + 2(-2)³ (substitution)

|8 - 8| + ∣-1 - 4| + 2(-8)

|0| + ∣-5| - 16

0 + 5 - 16 (absolute value of -5 = 5)

= -11