# How do you find the sum or difference of (5n-2p^2+2np)-(4p^2+4n)?

May 16, 2017

$- 6 {p}^{2} + n + 2 n p$

#### Explanation:

Remove the brackets first. The minus sign in front of the second bracket will change all of its signs.

$\left(5 n - 2 {p}^{2} + 2 n p\right) - \left(4 {p}^{2} + 4 n\right)$

$5 n - 2 {p}^{2} + 2 n p - 4 {p}^{2} - 4 n$

Now collect the like terms. You can re-arrange the expression to make this easier to see.

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

$= \textcolor{b l u e}{- 6 {p}^{2}} + \textcolor{red}{n} \textcolor{g r e e n}{+ 2 n p}$

(You only add or subtract the coefficients, the variables stay the same.)