# How do you add  (3b^4-3b^3+5b^2+13b-9) + (b^5+7b^3+2b^2-5b+4) + (-6b^4+b^2-3b-4)?

Jun 9, 2017

See a solution process below:

#### Explanation:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

$3 {b}^{4} - 3 {b}^{3} + 5 {b}^{2} + 13 b - 9 + {b}^{5} + 7 {b}^{3} + 2 {b}^{2} - 5 b + 4 - 6 {b}^{4} + {b}^{2} - 3 b - 4$

Next, group like terms:

${b}^{5} + 3 {b}^{4} - 6 {b}^{4} + 7 {b}^{3} - 3 {b}^{3} + 5 {b}^{2} + 2 {b}^{2} + {b}^{2} + 13 b - 5 b - 3 b - 9 + 4 - 4$

Now, combine like terms:

${b}^{5} + 3 {b}^{4} - 6 {b}^{4} + 7 {b}^{3} - 3 {b}^{3} + 5 {b}^{2} + 2 {b}^{2} + 1 {b}^{2} + 13 b - 5 b - 3 b - 9 + 4 - 4$

${b}^{5} + \left(3 - 6\right) {b}^{4} + \left(7 - 3\right) {b}^{3} + \left(5 + 2 + 1\right) {b}^{2} + \left(13 - 5 - 3\right) b + \left(- 9 + 4 - 4\right)$

${b}^{5} + \left(- 3\right) {b}^{4} + 4 {b}^{3} + 8 {b}^{2} + 5 b + \left(- 9\right)$

${b}^{5} - 3 {b}^{4} + 4 {b}^{3} + 8 {b}^{2} + 5 b - 9$