In the previous module, we have learned about terms of expression. Now, here, we will discuss the types of algebraic expressions which are monomials, binomials, trinomials, and polynomials.
Types of Algebraic Expressions
Let us start with monomials.
The word Monomial comes from mono meaning one and nominal (in this case meaning "term"); so, it says "one term". An expression with only one term is called a monomial. The expressions 7xy, � 5m, 3z2, 4, etc. are examples of monomials.
Now come to the binomial.
The word Binomial comes from bi (meaning "two") and nominal (in this case meaning "term"); so, it says "two terms". An expression that contains two unlike terms is called a binomial. The expressions x + y, m � 5, mn + 4m, a2 � b2 are examples of binomials.
Now, come to the trinomial.
Trinomial comes from tri (meaning "three") and nominal (in this case meaning "term"); so, it says "three terms".
An expression which contains three unlike terms is called a trinomial. The expressions x + y + 7, ab + a +b, 3x2 � 5x + 2, m + n + 10 are trinomials.
In the same ways; the polynomial word comes from poly- (meaning "many") and nominal (in this case meaning "term"), so it says "many terms". An expression with one or more unlike terms is called a polynomial.
In general, an expression with one or more terms is called a polynomial. Thus a monomial, a binomial and a trinomial are all polynomials.
Now, let us take an example to understand the types of algebraic expressions.
| S.No. | Expression | Type of Polynomial | Reason |
| 1. | 12x2y - 5yx2 | Monomial |
12x2y and -5yx2 are like terms |
| 2. | x + y - 7 | Trinomial | All terms are unlike terms |
| 3. | 2xy + 5x2y + 13z + 3xy2 | Polynomial | All terms are unlike terms |
| 4. | 3xyz + 5xy2 + 7yx2 | Binomial | 5xy2 and + 7yx2 are like terms. |
| 5. | 3xy + 7x - 13xy | Binomial | 3xy and -13xy are like terms |
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