Chapter 8.1, Problem 51PPE

To determine

To find: The simplified form of $\left(9p{q}^6-11p^{4}q\right)-\left(-5p{q}^6+p^4{q}^4\right)$ .

Answer to Problem 51PPE

The simplified form of $\left(9p{q}^6-11p^{4}q\right)-\left(-5p{q}^6+p^4{q}^4\right)$ is $14p{q}^6-11p^{4}q-p^4{q}^4$ .

Explanation of Solution

Given:

The expression is $\left(9p{q}^6-11p^{4}q\right)-\left(-5p{q}^6+p^4{q}^4\right)$ .

Calculation:

Simplify the expression $\left(9p{q}^6-11p^{4}q\right)-\left(-5p{q}^6+p^4{q}^4\right)$ as follows:

  $\begin{array}{c}\left(9p{q}^6-11p^{4}q\right)-\left(-5p{q}^6+p^4{q}^4\right)=9p{q}^6-11p^{4}q+5p{q}^6-p^4{q}^4\\ =9p{q}^6+5p{q}^6-11p^{4}q-p^4{q}^4\\ =14p{q}^6-11p^{4}q-p^4{q}^4\end{array}$

Thus, the simplified form of $\left(9p{q}^6-11p^{4}q\right)-\left(-5p{q}^6+p^4{q}^4\right)$ is $14p{q}^6-11p^{4}q-p^4{q}^4$ .