Evaluate Using the Given Value |4b-4|+|3-b^2|+2b^3 ; b=2

$| 4 b - 4 | + | 3 - b^{2} | + 2 b^{3}$ ; $b = 2$

Step 1

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

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

Step 2

Simplify each term.

Multiply $4$ by $2$ .

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

Subtract $4$ from $8$ .

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

The absolute value is the distance between a number and zero. The distance between $0$ and $4$ is $4$ .

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

Simplify each term.

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

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

Multiply $- 1$ by $4$ .

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

Subtract $4$ from $3$ .

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

The absolute value is the distance between a number and zero. The distance between $- 1$ and $0$ is $1$ .

$4 + 1 + 2 {(2)}^{3}$

Multiply $2$ by ${(2)}^{3}$ by adding the exponents.

Multiply $2$ by ${(2)}^{3}$ .

Raise $2$ to the power of $1$ .

$4 + 1 + 2^{1} {(2)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 + 1 + 2^{1 + 3}$

Add $1$ and $3$ .

$4 + 1 + 2^{4}$

Raise $2$ to the power of $4$ .

$4 + 1 + 16$

Step 3

Simplify by adding numbers.

Add $4$ and $1$ .

$5 + 16$

Add $5$ and $16$ .

$21$