Chapter 8.3, Problem 31PPS

To determine

To simplify: The expression $\left(m+2\right)\left[\left(m^2+3m-6\right)+\left(m^2-2m+4\right)\right]$

Answer to Problem 31PPS

  $2m^3+5m^2-4$

Explanation of Solution

Given:

  $\left(m+2\right)\left[\left(m^2+3m-6\right)+\left(m^2-2m+4\right)\right]$

Calculation:

The given expression is $\left(m+2\right)\left[\left(m^2+3m-6\right)+\left(m^2-2m+4\right)\right]$

Simplify the expression inside the square bracket

  $\left(m+2\right)\left(2m^2+m-2\right)$

Multiply each term of the first polynomial with each terms of the second polynomial and then simplify

  $\begin{array}{l}m\cdot 2m^2+m\cdot m+m\cdot \left(-2\right)+2\cdot 2m^2+2\cdot m+2\cdot \left(-2\right)\\ =2m^3+m^2-2m+4m^2+2m-4\\ =2m^3+5m^2-4\end{array}$

Therefore, the simplified expression is $2m^3+5m^2-4$