Question

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

Find the difference of $\left(w^2+w-42\right)$ and$\left(w^2-10w+24\right)$

Short answer

$\text{Thedifferenceof}\left(w^2+w-42\right)\text{and}\left(w^2-10w+24\right)\text{is}11w-66.$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionsare}\\ \left(w^2+w-42\right)\text{and}\left(w^2-10w+24\right)\\ \text{Wehavetofindthedifference}\\ i.e\text{Tofind:}\left(w^2+w-42\right)-\left(w^2-10w+24\right)\end{array}$

Step 2. Calculating the difference

$\begin{array}{l}\Rightarrow \left(w^2+w-42\right)-\left(w^2-10w+24\right)\\ =w^2+w-42-w^2+10w-24\left[\text{Rewritewithoutparentheses}\right]\\ =w^2-w^2+w+10w-42-24\left[\text{Combinetheliketerms}\right]\\ =11w-66\left[\text{Simplify}\right]\end{array}$