Chapter 14, Problem 18PT

To determine

To calculate: The simplified form of the polynomial $8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)$ .

Answer to Problem 18PT

The simplified form of the polynomial $8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)$ is $10x^3+25x^2-6x-10$ .

Explanation of Solution

Given Information:

The polynomialexpression is $8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)$ .

Calculation:

The given polynomial is $8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)$ .

Now, find the simplified form of the polynomial $8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)$ .

  $\begin{array}{c}8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)=8x^2\times x+8x^2\times 3+x\times 2x^2+x\times x-x\times 1-5\times x-5\times 2\\ =8x^3+24x^2+2x^3+x^2-x-5x-10\\ =10x^3+25x^2-6x-10\end{array}$

Hence, the simplified form of the polynomial $8x^2\left(x+3\right)+x\left(2x^2+x-1\right)-5\left(x-2\right)$ is $10x^3+25x^2-6x-10$ .