Evaluate Using the Given Value |-4b-8|+|-1-b^2|+2b^3 , b=-2

$| - 4 b - 8 | + | - 1 - b^{2} | + 2 b^{3}$ , $b = - 2$

Step 1

Replace the variable $b$ with $- 2$ in the expression.

$| - 4 \cdot - 2 - 8 | + | - 1 - {(- 2)}^{2} | + 2 {(- 2)}^{3}$

Step 2

Simplify each term.

Multiply $- 4$ by $- 2$ .

$| 8 - 8 | + | - 1 - {(- 2)}^{2} | + 2 {(- 2)}^{3}$

Subtract $8$ from $8$ .

$| 0 | + | - 1 - {(- 2)}^{2} | + 2 {(- 2)}^{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $0$ is $0$ .

$0 + | - 1 - {(- 2)}^{2} | + 2 {(- 2)}^{3}$

Simplify each term.

Raise $- 2$ to the power of $2$ .

$0 + | - 1 - 1 \cdot 4 | + 2 {(- 2)}^{3}$

Multiply $- 1$ by $4$ .

$0 + | - 1 - 4 | + 2 {(- 2)}^{3}$

Subtract $4$ from $- 1$ .

$0 + | - 5 | + 2 {(- 2)}^{3}$

The absolute value is the distance between a number and zero. The distance between $- 5$ and $0$ is $5$ .

$0 + 5 + 2 {(- 2)}^{3}$

Raise $- 2$ to the power of $3$ .

$0 + 5 + 2 \cdot - 8$

Multiply $2$ by $- 8$ .

$0 + 5 - 16$

Step 3

Simplify by adding and subtracting.

Add $0$ and $5$ .

$5 - 16$

Subtract $16$ from $5$ .

$- 11$