# Addition of Like algebraic terms

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

## Introduction

In algebraic mathematics, two or more like algebraic terms are connected by a plus sign for adding them mathematically. The like algebraic terms have a literal coefficient commonly and it is taken common from all the like terms in addition for calculating sum of them.

$2xy$, $3xy$ and $4xy$ are three like algebraic terms. The addition of them can be calculated in three simple steps.

#### First step

Write all the like terms in a row by displaying a plus sign between every two terms.
$2xy+3xy+4xy$

#### Second step

Take the literal coefficient common from all the terms.
$\implies$ $2xy+3xy+4xy$ $\,=\,$ ${(2+3+4)}xy$

#### Third step

Add all numerical coefficients and multiply it with their common literal coefficient.
$\,\,\, \therefore \,\,\,\,\,\,$ $2xy+3xy+4xy$ $\,=\,$ $9xy$

It can be observed that the sum of the like algebraic terms is also a like algebraic term. In this way, the addition of any two or more like algebraic terms is performed in algebra in three simple steps.

### Examples

Observe the following examples for understanding the addition of like algebraic terms much clear.

$(1)\,\,\,\,\,\,$ $3a+4a$ $\,=\,$ $(3+4)a$ $\,=\,$ $7a$

$(2)\,\,\,\,\,\,$ $d^2+2d^2+3d^2$ $\,=\,$ $(1+2+3)d^2$ $\,=\,$ $6d^2$

$(3)\,\,\,\,\,\,$ $6fg^2+3fg^2+11fg^2+7fg^2$ $\,=\,$ $(6+3+11+7)fg^2$ $\,=\,$ $27fg^2$

$(4)\,\,\,\,\,\,$ $7e^3d^4f^5+2e^3d^4f^5$ $\,=\,$ $(7+2)e^3d^4f^5$ $\,=\,$ $9e^3d^4f^5$

$(5)\,\,\,\,\,\,$ $2g+3g+7g+4g+5g$ $\,=\,$ $(2+3+7+4+5)g$ $\,=\,$ $21g$

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