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Example 3: Write the degrees of the following algebraic expressions:

1
3
3
4 4
2
3 2
(a) 12x + 7 (b) 5x – 6x + (c) m n + n m (d) p q – 7p – 2pq 2
3
Solution: (a) In the expression 12x + 7, the highest power of the variable x is 1 in term 12x. So, the
degree of the given polynomial is 1.
1
2
2
(b) In the expression 5x – 6x + , the highest power of the variable x is 2 in term 5x .
3
So, the degree of the given polynomial is 2.
3
3 2
(c) In the expression m n + n m, the highest power of polynomial is 3 + 2 = 5 in term
3 2
m n . So, the degree of the given polynomial is 5.
4 4
2
3
4 4
(d) In the expression p q – 7p – 2pq , the highest power is 4 + 4 = 8 in the term p q . So,
the degree of the given polynomial is 8.
Types of Polynomials
Constant Polynomial Linear Quadratic Cubic Biquadratic
Polynomial Polynomial Polynomial Polynomial
Definition A polynomial consisting A polynomial A polynomial A polynomial A polynomial
of a constant term only of degree of degree 2 of degree 3 is of degree 4
is called a constant 1 is called is called a called a cubic is called a
polynomial. The degree a linear quadratic polynomial. biquadratic
of a constant polynomial polynomial. polynomial. polynomial.
is zero.
2
3
2
4
3
2
Examples 8, –29, 6 5x – 1, 3 + 2x 6x – 5x + 1, x – 7x + 3x + 1, 5x – 7x + 4x
3
2
2y – 2y + 5 x – 5x – x + 8
Addition and Subtraction of Algebraic Expressions
Addition of Algebraic Expressions
While doing addition, we add the like terms and write the unlike terms as they are. So, when we
do the addition, we write each expression to be added in a separate row and write the like terms
one below the other and add them.
For example, add 8x + 4y + 3 and 7x – 4.
2
2
8x + 4y + 3
7x – 4 (Write the like terms one below the other)

15x + 4y – 1
2
Thus, the sum of two or more like terms is a like term whose numerical coefficient equals the sum
of the numerical coefficients of all the like terms being added and the literal factor is the same as
the literal factor of the given like terms.
Subtraction of Algebraic Expressions

To subtract an algebraic expression from another, we change the signs (from ‘+’ to –’ and ‘–’ to ‘+’)
of all the terms of the expression which is to be subtracted and then add the two expressions.

197 Algebraic Expressions