Evaluate Using the Given Value -2x^3-3x^2+4 for x=-2

$- 2 x^{3} - 3 x^{2} + 4$ for $x = - 2$

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

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

Simplify each term.

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

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

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

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

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

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

Add $1$ and $3$ .

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

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

$16 - 3 {(- 2)}^{2} + 4$

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

$16 - 3 \cdot 4 + 4$

Multiply $- 3$ by $4$ .

$16 - 12 + 4$

Simplify by adding and subtracting.

Subtract $12$ from $16$ .

$4 + 4$

Add $4$ and $4$ .

$8$