### Theory:

In the addition of algebraic expression, while adding algebraic expressions, we collect the like terms and add them. The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.
There are two ways to solve the addition of algebraic expressions:
• Horizontal Method
• Column Method
Horizontal Method: In this method, all expressions are written in a horizontal line, and then the terms are arranged to collect all the groups of like terms and then added.
Example:
Add $$6a + 8b - 7c$$, $$2b + c - 4a$$ and $$a - 3b - 2c$$.

$\left(6a\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}8b\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}7c\right) + \left(2b\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}c\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}4a\right) + \left(a\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}3b\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}2c\right)$

$=\phantom{\rule{0.147em}{0ex}}6a\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}8b\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}7c\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}2b\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}c\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}4a\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}a\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}3b\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}2c$

Arrange the like terms together, then add.

$=\phantom{\rule{0.147em}{0ex}}3a\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}7b\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}8c$

Thus, the required sum is $3a\phantom{\rule{0.147em}{0ex}}+\phantom{\rule{0.147em}{0ex}}7b\phantom{\rule{0.147em}{0ex}}-\phantom{\rule{0.147em}{0ex}}8c$.
Column Method: In this method, each expression is written in a separate row such that like terms are arranged one below the other in a column. Then the addition of terms is done column-wise.
Example:
Add $$6a + 8b - 7c$$, $$2b + c - 4a$$ and $$a - 3b - 2c$$.

Writing the terms of the given expression in the same order in the form of rows with like terms below each other and adding column-wise:

Thus, the sum of algebraic expressions is $3a+7b-8c$.