Question

$\text{Find the difference:}\left(8x^2+3x-19\right)-\left(7x^2-14\right)$

Short answer

The difference between the polynomials is$x^2+3x-5$

Step-by-step solution

Step 1. Given information 

$\begin{array}{l}\text{Thegivenpolynomialexpressionis}\\ \left(8x^2+3x-19\right)-\left(7x^2-14\right)\\ \text{Wehavetofindthedifference.}\end{array}$

Step 2. Distribute and identify like terms 

$\begin{array}{l}\text{Wehave}\left(8x^2+3x-19\right)-\left(7x^2-14\right)\\ \text{Distributeandidentifyliketermsandthenrearrangetheterms}\\ \Rightarrow \left(8x^2+3x-19\right)-\left(7x^2-14\right)=\underset{¯}{8x^2}+3x-19-\underset{¯}{7x^2}+14\\ =\left(8-7\right)x^2+3x-19+14\\ =x^2+3x-5\end{array}$