Question

$\text{Subtract}\left(m^2-7mn-3n^2\right)\text{from}\left(m^2+n^2\right)$

Short answer

On subtracting $\left(m^2-7mn-3n^2\right)\text{from}\left(m^2+n^2\right)$we get$7mn+4n^2$

Step-by-step solution

Step 1. Given information 

We have to subtract $\left(m^2-7mn-3n^2\right)\text{from}\left(m^2+n^2\right)$

This means we have to find

$\left(m^2+n^2\right)-\left(m^2-7mn-3n^2\right)$

Step 2. Distribute and identify like terms 

$\begin{array}{l}\text{Wehave}\left(m^2+n^2\right)-\left(m^2-7mn-3n^2\right)\\ \text{Distributeandidentifyliketermsandthenrearrangetheterms}\\ \Rightarrow \left(m^2+n^2\right)-\left(m^2-7mn-3n^2\right)=\underset{¯}{m^2}+\underset{¯}{\underset{¯}{n^2}}-\underset{¯}{m^2}+7mn+\underset{¯}{\underset{¯}{3n^2}}\\ =\left(m^2-m^2\right)+7mn+\left(n^2+3n^2\right)\\ =7mn+4n^2\end{array}$