Chapter 6.8, Problem 4PT

To determine

To calculate: The simplified form of $\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)$ ,

Answer to Problem 4PT

The simplified form of $\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)$ is $4x^3-x^2+10x-14$ .

Explanation of Solution

Given information:

The statement “ $\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)$ .”

Formula used:

When two or more functions are in subtraction then subtract the coefficient of $x^2$ to $x^2$ and coefficient of $x$ to $x$ and constant to constant ,

Consider the provided statement “ $\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)$ .”

Recall that When two or more functions are in subtraction then subtract the coefficient of $x^2$ to $x^2$ and coefficient of $x$ to $x$ and constant to constant ,

So, the given expression can be simplified as,

  $\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)$

Observe to solve the expression first open the brackets.

  $\begin{array}{l}\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)\\ 4x^3-x^2+5x-4+5x-10\end{array}$ .

Now solve the expression as the coefficient of $x^2$ to $x^2$ and coefficient of $x$ to $x$ and constant to constant:

  $\begin{array}{l}4x^3-x^2+5x+5x-4-10\\ 4x^3-x^2+10x-14\end{array}$

Since, $4x^3-x^2+10x-14$ cannot be simplified further,

Hence, the simplified form of $\left(4x^3-x^2+5x-4\right)+\left(5x-10\right)$ is $4x^3-x^2+10x-14$ .