Question

$\text{Subtract}\left(a^2+5ab-6b^2\right)\text{from}\left(a^2+b^2\right)$

Short answer

On subtracting $\left(a^2+5ab-6b^2\right)\text{from}\left(a^2+b^2\right)$we get$-5ab+7b^2$

Step-by-step solution

Step 1. Given information 

We have to$\text{subtract}\left(a^2+5ab-6b^2\right)\text{from}\left(a^2+b^2\right)$

Step 2. Distribute and identify like terms 

$\begin{array}{l}\text{Wehave}\left(a^2+b^2\right)-\left(a^2+5ab-6b^2\right)\\ \text{Distributeandidentifyliketermsandthenrearrangetheterms}\\ \Rightarrow \left(a^2+b^2\right)-\left(a^2+5ab-6b^2\right)=\underset{¯}{a^2}+\underset{¯}{\underset{¯}{b^2}}-\underset{¯}{a^2}-5ab+\underset{¯}{\underset{¯}{6b^2}}\\ =\left(a^2-a^2\right)-5ab+\left(b^2+6b^2\right)\\ \begin{array}{l}=0-5ab+7b^2\\ =-5ab+7b^2\end{array}\end{array}$