# How do you evaluate (5x ^ { 4} - 6x ^ { 3} + 4x ^ { 2} + 6x ) + ( - 10x ^ { 3} + 9x ^ { 2} + 10x - 8)?

Dec 2, 2017

$5 {x}^{4} - 16 {x}^{3} + 13 {x}^{2} - 4 x - 8$

#### Explanation:

First, just drop the parentheses:

$\textcolor{red}{5 {x}^{4}} - \textcolor{\mathmr{and} a n \ge}{6 {x}^{3}} + \textcolor{g r e e n}{4 {x}^{2}} + \textcolor{b l u e}{6 x} - \textcolor{\mathmr{and} a n \ge}{10 {x}^{3}} + \textcolor{g r e e n}{9 {x}^{2}} + \textcolor{b l u e}{10 x} - \textcolor{m a \ge n t a}{8}$

Now, we can rearrange the expression using the commutative to put like terms next to each other:

$\textcolor{red}{5 {x}^{4}} - \textcolor{\mathmr{and} a n \ge}{6 {x}^{3}} - \textcolor{\mathmr{and} a n \ge}{10 {x}^{3}} + \textcolor{g r e e n}{4 {x}^{2}} + \textcolor{g r e e n}{9 {x}^{2}} + \textcolor{b l u e}{6 x} - \textcolor{b l u e}{10 x} - \textcolor{m a \ge n t a}{8}$

Finally, combine like terms:

$\textcolor{red}{5 {x}^{4}} - \textcolor{\mathmr{and} a n \ge}{16 {x}^{3}} + \textcolor{g r e e n}{13 {x}^{2}} - \textcolor{b l u e}{4 x} - \textcolor{m a \ge n t a}{8}$