How much greater is (-13x^2 - 13x - 10) + (19x^2 - 19x - 5)?

Jun 19, 2015

Answer 1: =color(red)(-32x^2 + 6x-5
Answer 2:$= \textcolor{red}{6 {x}^{2}} \textcolor{b l u e}{- 32 x} - 15$

Explanation:

There are two ways of interpreting this question

1. How much greater is $- 13 {x}^{2} - 13 x - 10$ than $19 {x}^{2} - 19 x - 5$

Here we need to subtract:
$- 13 {x}^{2} - 13 x - 10$
$\textcolor{red}{-} 19 {x}^{2} \textcolor{red}{+} 19 x \textcolor{red}{+} 5$
=color(red)(-32x^2 + 6x-5

2.The second way is by adding the two as addition color(green)(+ has been mentioned in the question.

$- 13 {x}^{2} - 13 x - 10 + 19 {x}^{2} - 19 x - 5$

grouping like terms
$= \textcolor{red}{\left(- 13 {x}^{2} + 19 {x}^{2}\right)} + \textcolor{b l u e}{\left(- 13 x - 19 x\right)} + \left(- 10 - 5\right)$
$= \textcolor{red}{6 {x}^{2}} \textcolor{b l u e}{- 32 x} - 15$