Theory:

In the addition of algebraic expressions, 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.
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 p(x)=2x2+6x+5 and q(x)=3x22x1.
 
Start with: 2x2 + 6x + 5  +  3x2  2x  1
 
Place like terms together: 2x2+3x2  + 6x2x  +  51
 
Which is: (2+3)x2  (62)x  +  (51)
 
Add the like terms: 5x2  4x  + 4.
Column Method: In this method, each expression is written in a separate row such that the like terms are arranged one below other in a column. Then the addition of terms is done column-wise.
Example:
Add p(x)=2x2+6x+5 and q(x)=3x22x1.
 
2x2+6x+5+3x22x1(+)()()5x2+4x+4¯¯
Important!
The use of column method helps us to match the correct terms together in a complicated sum.