Identifying Terms and Co-efficient of an Expression

Terms and Co-efficients 

(VII CBSE Maths)

When terms have the same algebraic factors, they are like terms. When terms have different algebraic factors, they are unlike terms. 

For example, in the expression 2xy – 3x + 5xy – 4, look at the terms 2xy and 5xy. The factors of 2xy are 2, x and y. The factors of 5xy are 5, x and y.  Thus their algebraic (i.e., those which contain variables) factors are the same and hence they are like terms.

 On the other hand the terms 2xy and –3x, have different algebraic factors. They are unlike terms. Similarly, the terms, 2xy and 4, are unlike terms. Also, the terms –3x and 4 are unlike terms.

Terms and Co-efficient of an Algebraic Expression

An expression with only one term is called a monomial; for example, 7xy, – 5m, 3z2, 4 etc. 

An expression which contains two unlike terms is called a binomial; for example, x + y, m – 5, mn + 4m, a2 – b2 are binomials. 

An expression which contains three terms is called a trinomial; for example, the expressions x + y + 7, ab + a +b, 3x2 – 5x + 2, m + n + 10 are trinomials.

The expression ab + a + b + 5 is, however not a trinomial; it contains four terms and not three. The expression x +  y + 5x is not a trinomial as the terms x and 5x are like terms. 

In general, an expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials.