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Example 2: Identify the pairs with like terms:
Quick Check
2
2
13pqr, 13qrp; 51x y, 51y x; 5y, 7y; 99st, 99tu; 78rp, 99pq 2
Write two terms which
Solution: 13pqr, 13qrp; 5y, 7y are pairs with like terms since are like:
the terms have the same variables with equal exponents. 1. 3pq 2. 7xy 2

Types of Algebraic Expressions

An algebraic expressions have one or more than one term. Based on the number of unlike terms,
it can be classified as follows:

Monomials Binomials Trinomials
Definition An expression that contains An expression that contains An expression that contains
only one term is called a two terms is called a three terms is called a
monomial. binomial. trinomial.
5
2
Examples 6x, –9xy, −2 , yx 7x + 2y, x – y , xyz – 6, y – 8xy 2x y – 7xy + y , x + 4y – 5
2
2
2
2
3 4
Polynomials: In general, an expression that contains one or more terms with non-zero coefficient
is called polynomial, provided that the powers of its variables are non-negative integers. For
example, 8xyz, 2x + 3y, 8x + 5y + 4z + 8, etc.
Degree of a Polynomial

The degree of a polynomial is the highest exponent of the variable in the algebraic expression.
Degree of a Polynomial in One Variable

The highest power of the variable in a polynomial of one variable is called the degree of the

polynomial.

For example, (a) 4x + 5 is a polynomial of degree 1 as the highest power of variable x is 1.
3
(b) 6x + 5x – 2 is a polynomial of degree 3 as the highest power of variable x is 3.
Degree of a Polynomial in Two or More Variables

For a polynomial with two or more variables, we can find the degree of the polynomial by looking at
each term and summing up the powers of the variables.
Remember
The highest sum obtained from these represents the 1. A letter or a symbol having a fixed value
polynomial’s degree. is called constant.

3
2
For example, (a) x + 2y + 6xy + 7 is a polynomial of 2. Letters or symbols that do not have fixed
numerical values are called variables.
degree 3 as the highest power of 3. Terms having the same algebraic factors
variable x is 3. are called like factors.
4. Terms having different algebraic factors
(b) 2x y + xy + 7xy + 17 is a polynomial are called unlike factors.
3 2
3
of degree 5 as the highest power of 5. The highest power of a variable in any
variables x and y is the sum of 3 + 2 = 5. term is called the degree of a polynomial.

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