Subtraction of Like Algebraic Terms

A mathematical operation of subtracting two like algebraic terms is called the subtraction of like algebraic terms.

Introduction

In algebra, two like algebraic terms are connected by a minus sign to find the difference between them mathematically. In fact, the like algebraic terms have a common literal coefficient and it is taken common from both the terms to perform the subtraction successfully.

$2x^2y$ and $5x^2y$ are two two like algebraic terms. Take, $2x^2y$ is subtracted from $5x^2y$ and the subtraction can be done in three simple steps.

First step

Write $5x^2y$ first and then $2x^2y$ in a row but display a minus sign between them to represent the subtraction.
$5x^2y-2x^2y$

Second step

Take the literal coefficient common from both the terms.
$\implies$ $5x^2y-2x^2y$ $\,=\,$ ${(5-2)}x^2y$

Third step

Now, find the subtraction of the numbers and multiply the difference by their common literal coefficient.
$\,\,\, \therefore \,\,\,\,\,\,$ $5x^2y-2x^2y$ $\,=\,$ $3x^2y$

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

Examples

For better understanding the subtraction of algebraic terms, obverse the following examples.

$(1)\,\,\,\,\,\,$ $7a-5a$ $\,=\,$ $(7-5)a$ $\,=\,$ $2a$

$(2)\,\,\,\,\,\,$ $2bc-10bc$ $\,=\,$ $(2-10)bc$ $\,=\,$ $-8bc$

$(3)\,\,\,\,\,\,$ $3c^2-2c^2$ $\,=\,$ $(3-2)c^2$ $\,=\,$ $c^2$

$(4)\,\,\,\,\,\,$ $17d^3e^2f-23d^3e^2f$ $\,=\,$ $(17-23)d^3e^2f$ $\,=\,$ $-6d^3e^2f$

$(5)\,\,\,\,\,\,$ $5ghi-ghi$ $\,=\,$ $(5-1)ghi$ $\,=\,$ $4ghi$