Multiplication of Literals

A mathematical approach of multiplying two or more literal numbers for calculating their product is called the multiplication of literals.

Introduction

You learned how to multiply two or more numbers in arithmetic mathematics. You are about to study how to multiply a literal by another literal number. Possibly, there are two cases for multiplying the literals in algebra and let’s learn both the cases with examples to find their products.

Multiplying the same literals

Firstly, let’s learn how to multiply two same literal numbers.

$a \times a$

$a$ is a literal number and multiply it by the same literal number. There are two $a$ symbols in multiplication in this case. Their product is expressed simply in exponential notation by the exponentiation.

$\implies a \times a = a^2$

Examples

$(1) \,\,\,\,\,$ $b \times b \times b$ $\,=\,$ $b^3$

$(1) \,\,\,\,\,$ $c \times c \times c \times c$ $\,=\,$ $c^4$

$(3) \,\,\,\,\,$ $d \times d \times d \times d \times d$ $\,=\,$ $d^5$

Multiplying the different literals

Now, let’s find the product of the multiplication of the different literals.

$a \times b$

$a$ and $b$ are two different literals but their values are unknown. Therefore, it is not possible to calculate their product. Hence, the product of them is written as an expression simply by writing them one after one in a row.

$\implies$ $a \times b$ $\,=\,$ $a.b$

$\implies$ $a \times b$ $\,=\,$ $ab$

Examples

$(1) \,\,\,\,\,$ $x \times y \times z$ $\,=\,$ $xyz$

$(1) \,\,\,\,\,$ $a \times b \times c \times d$ $\,=\,$ $abcd$

$(3) \,\,\,\,\,$ $g \times h \times i \times j \times k$ $\,=\,$ $ghijk$

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