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Types of Algebraic Expression

Algebraic expressions are classified on the basis of the number of terms contained in them.

Monomial: An expression with only one term is called a monomial.
1
2
For example: 7x, –4xy, x y, –3xy , etc. are some examples Remember
2
4
of monomial expressions or monomials. A constant term is also a monomial.
1
1
0
0
Binomial: An expression which contains two unlike terms E.g., 2 as 2x , – 4 as p , etc.
4
is called a binomial.
2
For example: (2x + y), (p + 7), (a – b ), etc. are some examples of binomial expressions or binomials.
2
Trinomial: An expression which contains three unlike terms is called a trinomial.
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2
2
For example: (2x + 3y + 4z), (2p – q – r ), (a – 2ab + b ), etc. are some examples of trinomial
expressions or trinomials.
A monomial, a binomial and a trinomial, etc. are all polynomials.
Thus, an algebraic expression containing one or more terms is called a polynomial.
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2
2
7x, (9y + 3), a – 2ab + b , 3x y + 5xy – 2xy – 4, etc. are some examples of polynomials.
2
Always remember, in an algebraic expression, if the variable is in the denominator, the expression
will not be a polynomial.
2
21 + yz, 2 + 3 + 4 , l − 4mn , 5 , etc. are some examples of non-polynomial expressions.
,
xx a b c lmn xy x
++
Example 15: Classify the following algebraic expressions as monomial, binomial, and trinomial.
p 1 1
−
−7x + 3, + 2qr, 3xy − 2yz − zx, –100, x y, x + y, 3 – 7q + pr, 10a, a + b + c, t
2
3 2 2
1
2
Solution: –100, x y, 10a, and t are monomials as these expressions have only one term.
2
–7x + 3 and x + y are binomials as these expressions have two unlike terms.
p + 2 qr 3 xy 2 yz − 1 zx, 3 – 7q + pr, and a + b + c are trinomials as these expressions have three
,
−
−
3 2
unlike terms.

Maths Talk
How many algebraic expressions could you form by using –3, yz and 2z? Classify them. Also, check out the
algebraic expression you formed to justify the condition as a polynomial. Discuss why a polynomial is not formed
when an algebraic variable is in denominator.

Practice Time 5D

1. Write the terms and their irreducible factors in each of the given algebraic expressions.

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2
2 2
(a) 4xyz – 3x y (b) 8a b – 4 (c) 7 – 2pq (d) 7x – 11x + 3
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2
(e) 3p – 4pq + q – 5 (f) –3a b + 2ab – 6ab + 5
115 Introduction to Algebra