Subtraction of Algebraic expressions

A mathematical operation of subtracting an algebraic expression from another algebraic expression is called the subtraction of the algebraic expressions.

Introduction

In algebra, two algebraic expressions are involved in subtraction to find their difference mathematically. The subtraction of algebraic expressions is expressed by writing the expressions in a row but a minus sign is displayed between them. Then, the like algebraic terms of both expressions are subtracted to find their difference in mathematics.

$4x-6y+3z$
$12x+7y-21z$

First step

Write algebraic expressions in a row by displaying a minus sign between them

Assume, the expression $4x-6y+3z$ is subtracted from $12x+7y-21z$. So, write the algebraic expression $12x+7y-21z$ first and then $4x-6y+3z$ but display a minus sign between them.

$(12x+7y-21z)$ $-$ $(4x-6y+3z)$

$= \,\,\,$ $12x$ $+$ $7y$ $-$ $21z$ $-4x$ $+$ $6y$ $-$ $3z$

Second step

Now, write the like algebraic terms of both expressions closer.

$= \,\,\,$ $12x$ $-4x$ $+$ $7y$ $+$ $6y$ $-$ $21z$ $-$ $3z$

Third step

Merge the like algebraic terms by adding or subtracting the like algebraic terms.

$= \,\,\,$ $8x+13y-24z$

The difference of the expressions is an algebraic expression but its unlike terms cannot be added due to the property of unlikeness. Therefore, difference of any two expressions is also an algebraic expression and thus, the algebraic expressions are subtracted in algebra.