Q. 52 - Intermediate Algebra

Question

In the following exercise, find the difference of the polynomials. 

Find the difference of $\left(z^2-3z-18\right)$ and $\left(z^2+5z-20\right)$

Step-by-Step Solution

Answer

$\text{The difference of }\left(z^2-3z-18\right)\text{ and }\left(z^2+5z-20\right)\text{ is }-8z+2.$

Step 1. Given information

$\begin{array}{l}\text{The given expressions are}\\ \left(z^2-3z-18\right)\text{ and }\left(z^2+5z-20\right)\\ \text{We have to find the difference}\\ i.e\text{ To find : }\left(z^2-3z-18\right)-\left(z^2+5z-20\right)\end{array}$

Step 2. Calculating the difference

$\begin{array}{l}\Rightarrow \left(z^2-3z-18\right)-\left(z^2+5z-20\right)\\ =z^2-3z-18-z^2-5z+20\left[\text{Rewrite without parentheses}\right]\\ =z^2-z^2-3z-5z-18+20\left[\text{Combine the like terms}\right]\\ =-8z+2\left[\text{Simplify}\right]\end{array}$