Question

$\text{Add: (a)}8y^2+3z^2-3y^2\text{(b)}{m}^2{n}^2-8m^2+4n^2\text{.}$

Short answer

The result will be

$\begin{array}{l}a)5y^2+3z^2\\ b)m^2{n}^2-8m^2+4n^2\end{array}$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenpolynomialsare}\\ \text{(a)}8y^2+3z^2-3y^2\text{(b)}{m}^2{n}^2-8m^2+4n^2\text{.}\\ \text{Wehavetoaddtheterms}\end{array}$

Step 2. Solve part (a) 

$\begin{array}{l}\text{Wehave(a)}8y^2+3z^2-3y^2\text{.}\\ \text{Combinetheliketerms}\\ \Rightarrow 8y^2+3z^2-3y^2=\left(8-3\right)y^2+3z^3\\ =5y^2+3z^3\end{array}$

Step 3. Solve part (b) 

$\begin{array}{l}\text{Wehave(b)}{m}^2{n}^2-8m^2+4n^2\text{.}\\ \text{Combinetheliketerms}\\ \Rightarrow m^2{n}^2-8m^2+4n^2=m^2{n}^2-8m^2+4n^2\left[\text{Therearenoliketerms}\right]\end{array}$