Question

$\text{Simplify:}\left(p^3-p^{2}q\right)+\left(p{q}^2+q^3\right)-\left(p^{2}q+p{q}^2\right)$

Short answer

The simplified form of the given expression is$p^3-2p^{2}q+q^3$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenpolynomialexpressionis}\\ \left(p^3-p^{2}q\right)+\left(p{q}^2+q^3\right)-\left(p^{2}q+p{q}^2\right)\\ \text{Wehavetosimplifythegivenexpression.}\end{array}$

Step 2. Distribute and identify like terms 

$\begin{array}{l}\text{Wehave}\left(p^3-p^{2}q\right)+\left(p{q}^2+q^3\right)-\left(p^{2}q+p{q}^2\right)\\ \text{Distribute}\\ \Rightarrow \left(p^3-p^{2}q\right)+\left(p{q}^2+q^3\right)-\left(p^{2}q+p{q}^2\right)=p^3-p^{2}q+p{q}^2+q^3-p^{2}q-p{q}^2\\ \text{Identifyliketerms}\\ =p^3-\underset{¯}{p^{2}q}+\underset{¯}{\underset{¯}{p{q}^2}}+q^3-\underset{¯}{p^{2}q}-\underset{¯}{\underset{¯}{p{q}^2}}\\ \text{Rearrangetheterms}\\ =p^3+q^3-\underset{¯}{p^{2}q}-\underset{¯}{p^{2}q}+\underset{¯}{\underset{¯}{p{q}^2}}-\underset{¯}{\underset{¯}{p{q}^2}}\\ =p^3-2p^{2}q+q^3\end{array}$