# Terms, Factors and Coefficients of Expression:

## 1. Terms:

• Terms are added to form expressions. Terms are added to make an expression.

• For example, the terms 4x2 and (- 3xy) are added to give the expression 4x2 – 3xy. This is because 4x2 + (- 3xy) = 4x2 – 3xy.

• Note, the minus sign (–) is included in the term.

## 2. Factors:

A term is a product of factors. The term 4xy in the expression 4xy + 7 is a product of factors x, y, and 4. Factors containing variables are said to be algebraic factors.

The expression (4x2 – 3xy) consists of two terms 4x2 and – 3xy. The term 4x2 is a product of 4, x, and x; we say that 4, x, and x are the factors of the term 4x2. A term is a product of its factors. The term – 3xy is a product of the factors –3, x, and y.

## 3. Coefficient:

• The coefficient is the numerical factor in the term. Sometimes any one factor in a term is called the coefficient of the remaining part of the term.

• In the term 10xyz, 10 is the coefficient of xyz, in the term -7x2y2, - 7 is the coefficient of x2y2.

• When the coefficient of a term is + 1, it is usually omitted. For example, 1x is written as x; 1x2y2 is written as x2y2, and so on. Also, the coefficient (– 1) is indicated only by the minus sign.
Thus (– 1) x is written as – x; (–1) x2 y 2 is written as – x2 y2 and so on.
• Sometimes, the word 'coefficient' is used in a more general way. Thus we say that in the term 5xy, 5 is the coefficient of xy, x is the coefficient of 5y and y is the coefficient of 5x. In 10xy2, 10 is the coefficient of xy2, x is the coefficient of 10y2 and y2 is the coefficient of 10x.
Thus, in this more general way, a coefficient may be either a numerical factor or an algebraic factor or a product of two or more factors. It is said to be the coefficient of the product of the remaining factors.
If you would like to contribute notes or other learning material, please submit them using the button below.

### Shaalaa.com

Terms of Algebraic Expression [00:09:53]
S
0%