Chapter 12, Problem 4CLR

To determine

To Evaluate: The simplified value of the expression ${\left(ad\right)}^2-{\left(ad\right)}^3$ where $a=-1$ , $b=1$ , $c=0$ , $d=3$ and $e=-\frac{5}{2}$ .

Answer to Problem 4CLR

The value of the expression ${\left(ad\right)}^2-{\left(ad\right)}^3$ is $36$ .

Explanation of Solution

Given information:

The expression is ${\left(ad\right)}^2-{\left(ad\right)}^3$ and the values of variables are $a=-1$ , $b=1$ , $c=0$ , $d=3$ and $e=-\frac{5}{2}$ .

Formula used:

An algebraic expression may be replaced by numerical expression when the value of variable plugged in the expression.

The expression within the parentheses should be simplified first.

Calculation:

Consider the expression ${\left(ad\right)}^2-{\left(ad\right)}^3$ and values of variable $a=-1$ , $b=1$ , $c=0$ , $d=1$ and $e=-\frac{5}{2}$ .

Recall that an algebraic expression may be replaced by numerical expression when the value of variable plugged in the expression.

Use it, the expression ${\left(ad\right)}^2-{\left(ad\right)}^3$ replace as:

  ${\left(-1\times 3\right)}^2-{\left(-1\times 3\right)}^3$

Again recall that the expression within the parentheses should be simplified first,

Apply it,

  ${\left(-1\times 3\right)}^2-{\left(-1\times 3\right)}^3={\left(-3\right)}^2-{\left(-3\right)}^3$

Further simplify,

  $\begin{array}{c}{\left(-3\right)}^2-{\left(-3\right)}^3=9-\left(-27\right)\\ =9+27\\ =36\end{array}$

Thus, the value of the expression ${\left(ad\right)}^2-{\left(ad\right)}^3$ is $36$ .