Q. 5.10 - Intermediate Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given information

$\begin{array}{l}\text{The given polynomial expression is}\\ \left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)\\ \text{We have to find the difference.}\end{array}$

Step 2. Distribute and identify like terms

$\begin{array}{l}\text{We have}\left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)\\ \text{Distribute and identify like terms and then rearrange the terms}\\ \Rightarrow \left(9b^2-5b-4\right)-\left(3b^2-5b-7\right)=\underset{¯}{9b^2}-\underset{¯}{\underset{¯}{3b}}-4-\underset{¯}{3b^2}+\underset{¯}{\underset{¯}{5b}}+7\\ =\left(9-3\right)y^2+\left(-5+5\right)b-4+7\\ \begin{array}{l}=6b^2+0b+3\\ =6b^2+3\end{array}\end{array}$