Q. 58 - Intermediate Algebra

Question

In the following exercises, add or subtract the polynomials. 

$\left(m^2+2n^2\right)-\left(m^2-8mn-n^2\right)$

Step-by-Step Solution

Answer

Hence,

$\left(m^2+2n^2\right)-\left(m^2-8mn-n^2\right)=3n^2+8mn$

Step 1. Given information

$\begin{array}{l}\text{The given expressions is}\\ \left(m^2+2n^2\right)-\left(m^2-8mn-n^2\right)\\ \text{The sign between polynomials is }\text{'}-\text{'}.\end{array}$

Step 2. Subtract the polynomials

$\begin{array}{l}\Rightarrow \left(m^2+2n^2\right)-\left(m^2-8mn-n^2\right)\\ =m^2+2n^2-m^2+8mn+n^2\left[\text{Rewrite without parentheses}\right]\\ =m^2-m^2+2n^2+n^2+8mn\left[\text{Combine the like terms}\right]\\ =0+3n^2+8mn\left[\text{Simplify}\right]\\ =3n^2+8mn\end{array}$