Chapter 6.8, Problem 66S

To determine

To calculate: The simplified value of the expression $x^2\left(x-2\right)\left(x+1\right)$ .

Answer to Problem 66S

The simplified value of the expression $x^2\left(x-2\right)\left(x+1\right)$ is $x^4-x^3-2x^2$ .

Explanation of Solution

Given information:

The expression $x^2\left(x-2\right)\left(x+1\right)$ .

Formula used:

Distributive property states that $a\cdot \left(b+c\right)=ab+ac$ where a, b and c are real numbers.

Calculation:

Consider the expression $x^2\left(x-2\right)\left(x+1\right)$ .

Recall that the distributive property states that $a\cdot \left(b+c\right)=ab+ac$ where a, b and c are real numbers.

Apply it,

  $\begin{array}{c}{x}^2\left(x-2\right)\left(x+1\right)=x^2\left[x^2+x-2x-2\right]\\ =x^2\left[x^2-x-2\right]\\ =x^4-x^3-2x^2\end{array}$

Thus, the simplified value of the expression $x^2\left(x-2\right)\left(x+1\right)$ is $x^4-x^3-2x^2$ .