Multiplication of Literal numbers


The mathematical operation of multiplying a literal number by another literal number is called the multiplication of literal numbers.

Literals participate in multiplication in algebra and form algebraic terms as their product. The multiplication is same as the multiplication of numbers but product of the literals is determined by the character of the literal numbers.


In algebra, there are two special possible cases to multiply the literals.

Multiplying same literals

In this case, at least two same literals involve in multiplication and the product of them is expressed in exponential notation.

$(1) \,\,\,\,\,$ $a \times a$

For example, two same literals are engaged in multiplication and express them in exponential notation by writing the literal once and then the number of literal factors as its superscript.

In other words, $a \times a = a^2$

$(2) \,\,\,\,\,$ $b \times b \times b = b^3$

$(3) \,\,\,\,\,$ $c \times c \times c \times c = c^4$

Multiplying different literals

In this case also, at least two different literal numbers involve in multiplication but their product is written by writing all the different literals one after one.

$(1) \,\,\,\,\,$ $a \times b$

For example, $a$ and $b$ are two different literals and they cannot be written in exponential notation. So, the product of them is written as $ab$ or $ba$ in mathematics.

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

$(2) \,\,\,\,\,$ $a \times b \times c = abc$

$(3) \,\,\,\,\,$ $a \times b \times c \times d = abcd$

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