Addition of like algebraic terms

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

Introduction

In mathematics, it is essential for every learner to know the mathematical operation of performing summation with two or more like algebraic terms in some cases. Like algebraic terms have a literal factor commonly and it allows us to combine them as an algebraic term and it is also in the same form.

Example

$2xy$ and $3xy$ are two like algebraic terms. The addition of these two like algebraic terms can be done in two simple steps.

01

Display a Plus between terms

A plus sign should be displayed between every two like terms.

$2xy+3xy$

02

Obtain summation of them

Like algebraic terms have the same literal factor. So, take the literal factor common from them. In this example, $xy$ is the common literal factor of them.

$2xy+3xy = (2+3)xy$

Now, add the numbers and then multiply the sum of them by their common literal factor.

$\implies 2xy+3xy = 5xy$

More Examples

Observe the mathematical procedure in the following examples to learn how to add two or more like algebraic terms.

$(1)\,\,\,\,\,\,$ $3x^2+4x^2+5x^2$ $=$ $(3+4+5)x^2$ $=$ $12x^2$

$(2)\,\,\,\,\,\,$ $7abc+3abc$ $=$ $(7+3)abc$ $=$ $10abc$

$(3)\,\,\,\,\,\,$ $c^2d^2+20c^2d^2+11c^2d^2+5c^2d^2$ $=$ $(1+20+11+5)c^2d^2$ $=$ $37c^2d^2$

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

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



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