Evaluate Using the Given Value -b^2-2bx^2-x when x=-2

$- b^{2} - 2 b x^{2} - x$ when $x = - 2$

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

$- b^{2} - 2 b {(- 2)}^{2} - (- 2)$

Simplify each term.

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

Move ${(- 2)}^{2}$ .

$- b^{2} + {(- 2)}^{2} \cdot - 2 b - (- 2)$

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

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

$- b^{2} + {(- 2)}^{2} \cdot {(- 2)}^{1} b - (- 2)$

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

$- b^{2} + {(- 2)}^{2 + 1} b - (- 2)$

Add $2$ and $1$ .

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

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

$- b^{2} - 8 b - (- 2)$

Multiply $- 1$ by $- 2$ .

$- b^{2} - 8 b + 2$