### Theory:

A trinomial algebraic expression is an algebraic expression that has three terms.

The prefix 'tri' in 'trinomial' stands for $$3$$ terms.
To add two trinomials, you must:

1) remove the brackets (without changing the signs, because the “$$+$$” sign is in front of the brackets);
2) add the like terms.
Example:
$\left(-5{x}^{3}+3y-5{y}^{2}\right)+\left(8{x}^{3}+5{y}^{2}-2y\right)$
$\begin{array}{l}\left(-5{x}^{3}+3y-5{y}^{2}\right)+\left(8{x}^{3}+5{y}^{2}-2y\right)=\\ =-5{x}^{3}+3y-5{y}^{2}+8{x}^{3}+5{y}^{2}-2y.\end{array}$
$\begin{array}{l}\underset{¯}{-5{x}^{3}}+3y-5{y}^{2}\underset{¯}{+8{x}^{3}}+5{y}^{2}-2y=\\ \\ 3{x}^{3}\underset{¯}{+3y}-\overline{)5{y}^{2}}+\overline{)5{y}^{2}}\underset{¯}{-2y}=3{x}^{3}+y.\end{array}$