Question

In the following exercises, add or subtract the polynomials.

Short answer

Hence,

$\left(p^3-3p^{2}q\right)+\left(2p{q}^2+4q^3\right)-\left(3p^{2}q+p{q}^2\right)=5p^3-6p^{2}q+p{q}^2$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionsis}\\ \left(p^3-3p^{2}q\right)+\left(2p{q}^2+4q^3\right)-\left(3p^{2}q+p{q}^2\right)\\ \text{Wehavetoaddorsubtractthepolynomialsasapplicable.}\end{array}$

Step 2. Simplify

$\begin{array}{l}\Rightarrow \left(p^3-3p^{2}q\right)+\left(2p{q}^2+4q^3\right)-\left(3p^{2}q+p{q}^2\right)\\ =p^3-3p^{2}q+2p{q}^2+4q^3-3p^{2}q-p{q}^2\left[\text{Rewritewithoutparentheses}\right]\\ =p^3+4q^3-3p^{2}q-3p^{2}q+2p{q}^2-p{q}^2\left[\text{Combinetheliketerms}\right]\\ =5p^3-6p^{2}q+p{q}^2\left[\text{Simplify}\right]\end{array}$