Literals multiplication
Definition
The process of multiplying one literal by another to find their product is called the multiplication of literals.
What is the Multiplication of Literals?
A literal can be multiplied by another literal number to find their product. It is one of the basic operations in algebra, and the process involves multiplying one literal with another in a systematic way. This mathematical procedure is known as the multiplication of literals.
There are two different cases in multiplying literals, explained as follows.
- Multiplication of Literals in the Same Form
- Multiplication of Literals in Different Forms
In elementary mathematics, quantities are represented by numbers, but in algebra, they are denoted by literals. You have already learned how to multiply numbers in arithmetic; now it’s time to learn how to multiply one literal by another in algebra.
As a beginner, let’s learn every method of multiplying literals using simple, easy-to-understand examples.
How to multiply Literals in the Same Form
First, let’s study how to multiply literals of the same form using a simple numerical example.
Example
Evaluate $3 \times 3$
$\implies$ $3 \times 3$ $\,=\,$ $9$
The numbers being multiplied are the same, so their product can also be expressed in exponential form.
$\,\,\, \therefore \,\,\,$ $3 \times 3 \,=\, 3^2$
The value of a literal is unknown. When it is multiplied by itself, the product cannot be evaluated numerically, so it is expressed in exponential notation as follows.
Example
Evaluate $a \times a$
$\implies$ $a \times a \,=\, a^2$
Here are some more examples showing how to find the product of two or more literals.
- $b \times b \times b \,=\, b^3$
- $x \times x \times x \times x \,=\, x^4$
- $y \times y \times y \times y \times y \,=\, y^5$
How to multiply Literals in Different Forms
Now, let’s learn how to multiply different literals using a simple arithmetic example.
Example
Evaluate $2 \times 3$
$\implies$ $2 \times 3$ $\,=\,$ $6$
The numbers are different, and since the value of each is known, their product can be calculated.
Example
Evaluate $a \times b$
$\implies$ $a \times b \,=\, ab$
In this case, the literals are different and their values are unknown. Therefore, their product cannot be numerically evaluated. Instead, the multiplication is simply written as an expression.
The examples below show how to find the product of literals in different forms.
- $x \times y \times z$ $\,=\,$ $xyz$
- $a \times b \times c \times d$ $\,=\,$ $abcd$
- $g \times h \times i \times j \times k$ $\,=\,$ $ghijk$
Based on the two cases discussed above and their examples, you can now easily determine the product of two or more literals.