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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.


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.

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.


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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