# How do you combine like terms in (8x + 6x ^ { 3} - 2x ^ { 2} ) - ( x ^ { 4} - 8x ^ { 3} + x )?

##### 1 Answer
Apr 24, 2017

$- {x}^{4} + 14 {x}^{3} - 2 {x}^{2} + 7 x$

#### Explanation:

Each term with similar power can be combined

i.e. $\left(\textcolor{red}{8 x} + \textcolor{g r e e n}{6 {x}^{3}} - \textcolor{b l u e}{2 {x}^{2}}\right) - \left({x}^{4} - \textcolor{g r e e n}{8 {x}^{3}} + \textcolor{red}{x}\right)$

Distribute the negative

$\textcolor{red}{8 x} \textcolor{g r e e n}{+ 6 {x}^{3}} \textcolor{b l u e}{- 2 {x}^{2}} - {x}^{4} \textcolor{g r e e n}{+ 8 {x}^{3}} \textcolor{red}{- x}$

$\textcolor{red}{8 x - x} \textcolor{g r e e n}{+ 6 {x}^{3} + 8 {x}^{3}} \textcolor{b l u e}{- 2 {x}^{2}} - {x}^{4}$

$\textcolor{red}{7 x} \textcolor{g r e e n}{+ 14 {x}^{3}} \textcolor{b l u e}{- 2 {x}^{2}} - {x}^{4}$

Rearrange the expression according to the exponents (from highest to lowest)

$- {x}^{4} \textcolor{g r e e n}{+ 14 {x}^{3}} \textcolor{b l u e}{- 2 {x}^{2}} \textcolor{red}{+ 7 x}$