# How do you combine (5b ^ { 4} + 4b ^ { 2} + b ) - ( 2b ^ { 2} + 4b + 2b ^ { 4} )?

Jan 23, 2018

The simplified expression is $3 {b}^{4} + 2 {b}^{2} - 3 b$.

#### Explanation:

$\left(\textcolor{red}{5 {b}^{4}} + \textcolor{b l u e}{4 {b}^{2}} + \textcolor{g r e e n}{b}\right) - \left(\textcolor{b l u e}{2 {b}^{2} + \textcolor{g r e e n}{4 b} + \textcolor{red}{2 {b}^{4}}}\right)$

Distribute the negative sign to the second parenthetical term and get rid of the parentheses:

$\textcolor{red}{5 {b}^{4}} + \textcolor{b l u e}{4 {b}^{2}} + \textcolor{g r e e n}{b} - \textcolor{b l u e}{2 {b}^{2}} - \textcolor{g r e e n}{4 b} - \textcolor{red}{2 {b}^{4}}$

Rearrange so like terms are together:

$\textcolor{red}{5 {b}^{4}} - \textcolor{red}{2 {b}^{4}} + \textcolor{b l u e}{4 {b}^{2}} - \textcolor{b l u e}{2 {b}^{2}} + \textcolor{g r e e n}{b} - \textcolor{g r e e n}{4 b}$

Combine like terms:

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