Question

In the following exercises, add or subtract the polynomials.

$\left(a^2-b^2\right)-\left(a^2+3ab-4b^2\right)$

Short answer

Hence,

$\left(a^2-b^2\right)-\left(a^2+3ab-4b^2\right)=3b^2-3ab$

Step-by-step solution

Step 1. Given information

$\begin{array}{l}\text{Thegivenexpressionsis}\\ \left(a^2-b^2\right)-\left(a^2+3ab-4b^2\right)\\ \text{Thesignbetweenpolynomialsis}\text{'}-\text{'}.\\ \text{Thus,Wehavetosubtractthepolynomials.}\end{array}$

Step 2. Subtract the polynomials

$\begin{array}{l}\Rightarrow \left(a^2-b^2\right)-\left(a^2+3ab-4b^2\right)\\ =a^2-b^2-a^2-3ab+4b^2\left[\text{Rewritewithoutparentheses}\right]\\ =a^2-a^2-b^2+4b^2-3ab\left[\text{Combinetheliketerms}\right]\\ =0+3b^2-3ab\left[\text{Simplify}\right]\\ =3b^2-3ab\end{array}$