A mathematical operation of subtracting an algebraic expression from another algebraic expression is called the subtraction of the algebraic expressions.
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.
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.
$(12x+7y-21z)$ $-$ $(4x-6y+3z)$
$= \,\,\,$ $12x$ $+$ $7y$ $-$ $21z$ $-4x$ $+$ $6y$ $-$ $3z$
Now, write the like algebraic terms of both expressions closer.
$= \,\,\,$ $12x$ $-4x$ $+$ $7y$ $+$ $6y$ $-$ $21z$ $-$ $3z$
$= \,\,\,$ $8x+13y-24z$
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.
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