# Addition of Like Algebraic Terms

## Definition

A mathematical operation of adding two or more like algebraic terms is called the addition of like algebraic terms.

The addition of like algebraic terms is also called as summation of like algebraic terms.

Like terms have a common literal coefficient. So, two or more like terms can be added directly by adding numeral coefficients of them. The addition of all like terms combine them as an algebraic term but it also consists of same literal coefficient in the term..

### Procedure

$mn^{\displaystyle 2}$, $2mn^{\displaystyle 2}$, $4mn^{\displaystyle 2}$ and $5mn^{\displaystyle 2}$ are four algebraic terms. All four terms have $mn^{\displaystyle 2}$ commonly as literal coefficient. So, they are like terms. Write all four terms one after one but place a plus sign between every two like terms to perform the addition.

$mn^{\displaystyle 2} + 2mn^{\displaystyle 2} + 4mn^{\displaystyle 2} + 5mn^{\displaystyle 2}$

$= 1mn^{\displaystyle 2} + 2mn^{\displaystyle 2} + 4mn^{\displaystyle 2} + 5mn^{\displaystyle 2}$

$= (1 + 2 + 4 + 5)mn^{\displaystyle 2}$

$\therefore \,\, mn^{\displaystyle 2} + 2mn^{\displaystyle 2} + 4mn^{\displaystyle 2} + 5mn^{\displaystyle 2} = 12mn^{\displaystyle 2}$

In this example, four like terms are added and combined as an algebraic term as their total. The term obtained from the total ($12mn^{\displaystyle 2}$) also consists of $mn^{\displaystyle 2}$ as literal coefficient. So, it is also a like term.

Observe the following more examples to learn how to add like terms algebraically.

#### Examples

$(1) \,\,\,\, a + a = 2a$

$(2) \,\,\,\, 3x^{\displaystyle 2} + 4x^{\displaystyle 2} + 7x^{\displaystyle 2} = 15x^{\displaystyle 2}$

$(3) \,\,\,\, p^{\displaystyle 3}q^{\displaystyle 2}r + 8p^{\displaystyle 3}q^{\displaystyle 2}r = 9p^{\displaystyle 3}q^{\displaystyle 2}r$

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