Chapter 6, Problem 1T

To determine

The value of the algebraic equation for the given value of variable.

Answer to Problem 1T

Solution: $-44$

Explanation of Solution

Given: $x^3-4{\left(x-1\right)}^2\text{when }x=-2$

Explanation:

Put $x=-2$ in the given expression and simplify it as follows:

$\begin{array}{c}{x}^3-4{\left(x-1\right)}^2={\left(-2\right)}^3-4{\left(-2-1\right)}^2\\ =-8-4{\left(-3\right)}^2\\ =-8-36\\ =-44\end{array}$

Hence, the expression $x^3-4{\left(x-1\right)}^2$ evaluated at $x=-2$ gives $-44$.