# How much greater is (-10x^6 + 18x^3 + 13) + (7x^6 - 7x^2 + 17)?

Jun 19, 2015

answer 1 = color(red)(-17x^6 + 18x^3 + 7x^2 -4
answer 2 = color(red)(-3x^6 +18x^3 - 7x^2+30

#### Explanation:

There are two interpretations for the above question:

• How much greater is $\left(- 10 {x}^{6} + 18 {x}^{3} + 13\right)$than $\left(7 {x}^{6} - 7 {x}^{2} + 17\right)$

Here we need to subtract:
$- 10 {x}^{6} + 18 {x}^{3} + 13$
$\textcolor{red}{-} 7 {x}^{6} \textcolor{red}{+} 7 {x}^{2} \textcolor{red}{-} 17$
 = color(red)(-17x^6 + 18x^3 + 7x^2 -4

• Grouping like terms and adding the two expressions :

$= \textcolor{red}{\left(- 10 {x}^{6} + 7 {x}^{6}\right)} + 18 {x}^{3} - 7 {x}^{2} + \textcolor{b l u e}{\left(13 + 17\right)}$
$= \textcolor{red}{- 3 {x}^{6}} + 18 {x}^{3} - 7 {x}^{2} + \textcolor{b l u e}{30}$