Chapter 6.8, Problem 3PT

To determine

To calculate: The simplified form of $\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)$ ,

Answer to Problem 3PT

The simplified form of $\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)$ is $-2x^2+10x-5$ .

Explanation of Solution

Given information:

The statement “ $\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)$ .”

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 “ $\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)$ .”

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,

  $\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)$

Observe to solve the expression.

  $\begin{array}{l}\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)\\ 2x^2+3x-4-4x^2+7x-1\\ 2x^2-4x^2+3x+7x-4-1\\ -2x^2+10x-5\end{array}$ .

Since, $-2x^2+10x-5$ cannot be simplified further,

Hence, the simplified form of $\left(2x^2+3x-4\right)-\left(4x^2-7x+1\right)$ is $-2x^2+10x-5$ .