Math Doubts

Literals’ Multiplication

Definition

The process of multiplying a literal by another literal to find their product is called the multiplication of literals.

What is Multiplication of Literals?

A literal number is connected to another literal mathematically by a multiplication symbol. It is a basic math operation in algebra and it is used mainly to find the product of two or more literals. There is a mathematical procedure in algebra to find the product of literal numbers and it is called the multiplication of literals.

If you are a beginner, you should firstly know how to multiply a literal by another literal number. There are two different cases in multiplying the literals numbers in algebra.

  1. Multiplication of Like literals
  2. Multiplication of Unlike literals

So, let’s learn each case for finding the product of two or more literal numbers in algebra.

Case1

How to multiply Like literals

In elementary mathematics, the quantities are expressed by numbers, whereas they are denoted by literals in advanced mathematics.

Firstly, let’s learn how to multiply a quantity by same quantity from an arithmetic example.

Example

In this example, a number $3$ is multiplied by itself and their product can be evaluated arithmetically.

$3 \times 3 \,=\, 9$

The numbers in the multiplication are same. So, their product can also be expressed in exponential form.

$\therefore \,\,\,$ $3 \times 3 \,=\, 3^2$

However, the value of a literal is unknown. So, it is not possible to find the product of like literals. However, the product of like literal numbers can be written in exponential notation as follows.

Example

$a \times a \,=\, a^2$

The above simple example explains that when a literal is multiplied by itself, their product is written in exponential notation and it is equal to the literal raised to the power of the number of literals are involved in multiplication.

  1. $b \times b \times b \,=\, b^3$
  2. $x \times x \times x \times x \,=\, x^4$
  3. $y \times y \times y \times y \times y \,=\, y^5$

Now, you can multiply the like literals as explained above and also find their product easily.

Case2

How to multiply Unlike literals

Now, multiply a number by another number to find their product mathematically.

Example

$2 \times 3 \,=\, 6$

In this case, two different numbers are involved in multiplication and their quantities are known. So, it is possible to find their product but it is not possible to express their product in exponential form.

Example

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

The quantities of different literals $a$ and $b$ are unknown. So, it is not possible to find their product mathematically and it is also not possible to express their product in exponential notation. However, the multiplication of unlike literal numbers is simply written as their product.

  1. $x \times y \times z$ $\,=\,$ $xyz$
  2. $a \times b \times c \times d$ $\,=\,$ $abcd$
  3. $g \times h \times i \times j \times k$ $\,=\,$ $ghijk$

You can now multiply any two or more literal numbers as per the above two cases and find the product of them easily.