# Literal coefficient

## Definition

A coefficient in literal form in an algebraic term is called a literal coefficient.

In mathematics, a coefficient is basically a multiplicative factor in a term but in algebra, a literal coefficient is a multiplying factor which contains one or product of more literal numbers in an algebraic term.

### Examples

$(1) \,\,\,\,\,$ $7a$

The algebraic term $7a$ can be written as $7a = 7 \times a$. The figure $7$ is a multiplying factor but a number and $a$ is also a multiplying factor but a literal number.

Therefore, the multiplying literal $a$ is called as a literal coefficient of $7$ in the algebraic term $7a$.

$(2) \,\,\,\,\,$ $2xy$

The algebraic term $2xy$ is formed by the number $2$, and literals $x$ and $y$.

1. The algebraic term $2xy$ can be written as $2xy = 2x \times y$.
The literal $y$ is called as a literal coefficient of $2x$ and the product $2x$ is also called as a literal coefficient of $y$ in algebraic term $2xy$.
2. The algebraic term $2xy$ can be written as $2xy = 2y \times x$.
The literal $x$ is called as a literal coefficient of $2y$ and the product $2y$ is also called as a literal coefficient of $x$ in algebraic term $2xy$.
3. The algebraic term $2xy$ can also be written as $2xy = 2 \times xy$.
The product of literals $xy$ is called as a literal coefficient of $2$ but the number $2$ cannot be a literal coefficient of $xy$ in algebraic term $2xy$ because it is a number.

$(3)$ $\,\,\, -p^{\displaystyle 2}q$

The algebraic term $-p^2q$ is known as $-1p^2q$.

1. The algebraic term $–p^2q$ is written as $-p^2q = -p^2 \times q$.
The literal $q$ is called as a literal coefficient of $-p^2$ and the literal $p$ with an exponent $2$, which means $-p^2$ is also called as a literal coefficient of $q$.
2. The algebraic term $–p^2q$ is written as $-p^2q = p^2 \times -q$.
The literal $-q$ is called as a literal coefficient of $p^2$ and the product of the literals $p^2$ is also called as a literal coefficient of $-q$.
3. The algebraic term $–p^2q$ is written as $-p^2q = -1 \times p^2q$.
The product of literals $p^2q$ is called as a literal coefficient of $-1$ but $-1$ cannot be called as a literal coefficient of $p^2q$ because it is a number.
4. The algebraic term $–p^2q$ is written as $-p^2q = 1 \times -p^2q$.
The product of literals $-p^2q$ is called as a literal coefficient of $1$ but $1$ is not a literal coefficient of $-p^2q$ because it is a number.
5. The algebraic term $–p^2q$ is written as $-p^2q = p \times -pq$.
The literal number $p$ is a literal coefficient of $-pq$ and the product of literals $-pq$ is also a literal coefficient of $p$.
6. The algebraic term $–p^2q$ is written as $-p^2q = -p \times pq$.
The literal number $-p$ is a literal coefficient of $pq$ and the product of literals $pq$ is also a literal coefficient of $-p$.

The examples clear that a literal coefficient can be a literal number, product of different literals, a literal with an exponent or product of literals with exponents and at least one other literal.

Remember, all literal factors are literal coefficients of remaining multiplying factors in algebraic terms but all literal coefficients are not literal factors algebraically.