Question

$\text{Find the}\text{:difference}\left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)$

Short answer

The difference of the given polynomials is$6b^2+3$

Step-by-step solution

Step 1. Given information  

$\begin{array}{l}\text{Thegivenpolynomialexpressionis}\\ \left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)\\ \text{Wehavetofindthedifference.}\end{array}$

Step 2. Distribute and identify like terms

$\begin{array}{l}\text{Wehave}\left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)\\ \text{Distributeandidentifyliketermsandthenrearrangetheterms}\\ \Rightarrow \left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)=\underset{¯}{9b^2}-\underset{¯}{\underset{¯}{3b}}-4-\underset{¯}{3b^2}+\underset{¯}{\underset{¯}{5b}}+7\\ =\left(9-3\right)y^2+\left(-5+5\right)b-4+7\\ \begin{array}{l}=6b^2+0b+3\\ =6b^2+3\end{array}\end{array}$