Monomials, Binomials, Trinomials and Polynomials
An expression with only one term is called a monomial; for example, 7xy, – 5m
An expression which contains two unlike terms is called a binomial.
For example, x + y, m – 5, mn + 4m,
An expression which contains three terms is called a trinomial; for example, the expressions x + y + 7, ab + a +b,
The expression ab + a + b + 5 is, however not a trinomial; it contains
In general, an expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials.
Try these
Classify the following expressions as a monomial, a binomial or a trinomial: a, a + b, ab + a + b, ab + a + b – 5, xy, xy +5,
Example 3
State with reasons, which of the following pairs of terms are of like terms and which are of unlike terms:
(i) 7x, 12y (ii) 15x, –21x (iii) – 4ab, 7ba (iv) 3xy, 3x
(v)
Solution :
| S.No | Pair | Factors | Algebraic factors same or different | Like / Unline terms | Remarks |
|---|---|---|---|---|---|
| (i) | 7x, 12y | 7, x 12,y | The variables in the terms are different. | ||
| (ii) | 15x, -21x | 15, x-21,x | |||
| (iii) | – 4ab, 7 ba | – 4, a, b 7,b,a | Remember ab=ba | ||
| (iv) | 3xy , 3x | 3, x, y 3,x | The variable y is only in one term. | ||
| (v) | 6x | 6, x, y, y 9, x, x, y | The variables in the two terms match, but their powers do not match. | ||
| (vi) | p | 1, p, q, q – 4, p, q, q | Note, numerical factor 1 is not shown |
Following simple steps will help you to decide whether the given terms are like or unlike terms:
(i) Ignore the numerical coefficients. Concentrate on the algebraic part of the terms.
(ii) Check the variables in the terms. They must be the same.
(iii) Next, check the powers of each variable in the terms. They must be the same. Note that in deciding like terms, two things do not matter (1) the numerical coefficients of the terms and (2) the order in which the variables are multiplied in the terms