Q. 5.5 - Intermediate Algebra

Question

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

Step-by-Step Solution

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 1. Given information

$\begin{array}{l}\text{The given polynomials are}\\ \text{ (a) }8y^2+3z^2-3y^2\text{ (b) }{m}^2{n}^2-8m^2+4n^2\text{. }\\ \text{We have to add the terms}\end{array}$

Step 2. Solve part (a)

$\begin{array}{l}\text{We have (a) }8y^2+3z^2-3y^2\text{.}\\ \text{Combine the like terms}\\ \Rightarrow 8y^2+3z^2-3y^2=\left(8-3\right)y^2+3z^3\\ =5y^2+3z^3\end{array}$

Step 3. Solve part (b)

$\begin{array}{l}\text{We have (b) }{m}^2{n}^2-8m^2+4n^2\text{.}\\ \text{Combine the like terms}\\ \Rightarrow m^2{n}^2-8m^2+4n^2=m^2{n}^2-8m^2+4n^2\left[\text{There are no like terms}\right]\end{array}$