Chapter 8.3, Problem 36P

Simplify each product.

$\left(m^2-2m+7\right)(3m+6)$

To determine

To simplify: $(m^2-2m+7)(3m+6)$

Answer to Problem 36P

  $3m^3+9m+42$

Explanation of Solution

Given information: $(m^2-2m+7)(3m+6)$

Calculation:

  $\begin{array}{l}(m^2-2m+7)(3m+6)\\ =m^2\cdot (3m+6)+(-2m)\cdot (3m+6)+7\cdot (3m+6)\\ =m^2\cdot 3m+m^2\cdot 6+(-2m)\cdot 3m+(-2m)\cdot 6+7\cdot 3m+7\cdot 6\\ =3m^3+6m^2-6m^2-12m+21m+42\\ =3m^3+0+9m+42\\ =3m^3+9m+42\end{array}$

Thus, $(m^2-2m+7)(3m+6)=3m^3+9m+42$