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Terms of an Algebraic Expressions

Let us observe an algebraic expressions 2xy + 5. It has two parts,
i.e., 2xy and 5. Both parts are separated by the operation ‘+’. Remember

These parts are the terms of this algebraic expression 2xy + 5. Operations multiplication (×)
and division (÷) do not separate
2
2
Let us take another example, a – 2ab + b , here a , – 2ab, and b the terms, so 4 × xy = 4xy or
2
2
2
2
are three terms separated by the operations ‘+’ and ‘–’. a ÷ b = a are considered as a
b
Thus, the various parts of an algebraic expression which are single term.
separated by the arithmetical operations: addition (+) and
subtraction (–) are called the terms of the algebraic expression.
Example 11: Write all the terms in the following algebraic expressions:
1
(a) 2p – 5q + 3 (b) 3xy + 2y – xy (c) a – 3ab – b + 1 (d) 4m – 2lmn
2

Solution: 2
Algebraic Expressions Terms
(a) 2p – 5q + 3 2p, – 5q, and 3

(b) 3xy + 2y – xy 3xy, 2y, and – xy

1 1

(c) a – 3ab – b + 1 a, – 3ab, – b, and 1
2 2
2
(d) 4m –2 lmn 4m , –2 lmn
2
Factors of a Term

3
Let us take an algebraic expression 2x – 3xyz. Remember
3
3
It consists of two terms 2x and –3xyz. The term 2x is a product When a factor cannot be factorised
of 2, x, x and x; and –3xyz is the product of –3, x, y and z. further, it is called an irreducible
factor. E.g., –3, x, y and z are
3
So, we say that 2, x, x, and x are the factors of the term 2x and irreducible factors of the term –3xyz.
–3, x, y, and z are the factors of the term –3xyz.

Hence, a term is a product of all its factors.
3
We can represent the terms and factors of the terms of Algebraic Expression 2x – 3xyz
an algebraic expression conveniently and elegantly by Terms 2x 3 –3xyz

a tree diagram.
Factors 2 x x x –3 x y z
3
The tree diagram for the expression 2x – 3xyz is as
shown in the adjacent figure.
Example 12: Write irreducible factors of each term in the following algebraic expressions.

(a) –ab + 2b – 3a (b) 5xy + 7x y
2
2
4 3
2
3
2
(c) 5x – 3xy + 2x (d) x − xy + 5y 2
5 4
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