Subtraction of Literals

A mathematical approach of subtracting a literal by another literal number for calculating their difference is called the subtraction of literals.

Introduction

In arithmetic, you have learned how to subtract any two numbers. Now, you are going to learn how to subtract a literal from another. There are two cases for subtracting the literal numbers and let us learn both the cases to understand the process for finding the difference of the literals.

Subtracting same literals

Let us learn how to subtract two same literal numbers.

$a-a$

$a$ is a literal number and subtract it by same literal. There are two $a$ symbols in this case. Actually, the value of $a$ is unknown but their difference is zero because they both have same value.

$\implies a-a = 0$

The subtraction of the literals can also be proved in arithmetic.

$a-a$ $\,=\,$ $1 \times a -1 \times a$

$\implies$ $a-a$ $\,=\,$ $a \times (1-1)$

$\implies$ $a-a$ $\,=\,$ $a \times 0$

$\implies$ $a-a$ $\,=\,$ $0 \times a$

$\,\,\, \therefore \,\,\,\,\,\,$ $a-a$ $\,=\,$ $0$

Examples

$(1) \,\,\,\,\,$ $d-d \,=\, 0$

$(2) \,\,\,\,\,$ $k-k \,=\, 0$

$(3) \,\,\,\,\,$ $y-y \,=\, 0$

Subtracting different literals

Let’s learn how to subtract two different literal numbers.

$a-b$

$a$ and $b$ are two different literal numbers, and their values are unknown. Hence, it is impossible to find their difference. So, the subtraction of them is simply written as an expression in algebra.

Examples

$(1) \,\,\,\,\,$ $c-d$

$(2) \,\,\,\,\,$ $h-i$

$(3) \,\,\,\,\,$ $x-y$

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