Chapter 8.2, Problem 39PPS

To determine

To simplify: The expression $-5q^2{w}^3\left(4q+7w\right)+4q{w}^2\left(7q^{2}w+2q\right)-3qw\left(3q^2{w}^2+9\right)$

Answer to Problem 39PPS

  $-q^3{w}^3-35q^2{w}^4+8q^2{w}^2-27qw$

Explanation of Solution

Given:

  $-5q^2{w}^3\left(4q+7w\right)+4q{w}^2\left(7q^{2}w+2q\right)-3qw\left(3q^2{w}^2+9\right)$

Calculation:

The given expression is

  $-5q^2{w}^3\left(4q+7w\right)+4q{w}^2\left(7q^{2}w+2q\right)-3qw\left(3q^2{w}^2+9\right)$

Remove the parenthesis

  $-5q^2{w}^3\cdot 4q-5q^2{w}^3\cdot 7w+4q{w}^2\cdot 7q^{2}w+4q{w}^2\cdot 2q-3qw\cdot 3q^2{w}^2-3qw\cdot 9$

Simplify the expression

  $-20q^3{w}^3-35q^2{w}^4+28q^3{w}^3+8q^2{w}^2-9q^3{w}^3-27qw$

Combine the like terms

  $\begin{array}{l}-20q^3{w}^3+28q^3{w}^3-9q^3{w}^3-35q^2{w}^4+8q^2{w}^2-27qw\\ =-q^3{w}^3-35q^2{w}^4+8q^2{w}^2-27qw\end{array}$