Chapter 4.2, Problem 25E

To determine

To describe: and correct the error in performing the operation.

Answer to Problem 25E

  $\left(x^2-3x+4\right)-\left(x^3+7x-2\right)=-x^3+x^2+4x+6$

Explanation of Solution

Given information:

An expression is given as

  $\left(x^2-3x+4\right)-\left(x^3+7x-2\right)$

Performed calculation is shown below:

  $\begin{array}{c}\left(x^2-3x+4\right)-\left(x^3+7x-2\right)=x^2-3x+4-x^3+7x-2\\ =-x^3+x^2+4x+2\end{array}$

Calculation:

Consider the expression and simplify by grouping like terms as shown:

  $\begin{array}{c}\left(x^2-3x+4\right)-\left(x^3+7x-2\right)=x^2-3x+4-x^3-7x+2\\ =x^2-x^3-3x-7x+4+2\\ =-x^3+x^2-10x+6\end{array}$

The error is described below:

In second step plus sign has been used instead of minus sign before the term $7x$ and minus sign has been used instead of plus sign before 2.

The correct answer will be $-x^3+x^2+4x+6$ .