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Solution:

(a) Algebraic Expression –ab + 2b – 3a

Terms –ab 2b –3a

Factors –1 a b 2 b –3 a

(b) Algebraic Expression 5xy + 7x y
2
2
Terms 5xy 2 7x y
2

Factors 5 x y y 7 x x y

(c) Algebraic 3 2 (d) Algebraic 4 x – 3 2
2
Expression 5x – 3xy + 2x Expression 5 4 xy + 5y
Terms 5x 3 –3xy 2x 2 Terms 4 2 3
4
5 x − xy 5y 2
Factors 5 x x x –3 x y 2 x x
Factors 4 x − 3 x y 5 y y
5 x 4
Coefficient

We have learnt how to write a term of an algebraic expression as a product of factors.
Factors may be numerical and algebraic (variable).

The numerical factor is said to be the numerical coefficient Remember
or simply the coefficient of the term. When the coefficient of a term is +1,
it is usually omitted. E.g., 1x is written
For example, in 7xy – 2x, 7 is the numerical coefficient of the as x; 1x y is written as x y and so
2 2
2 2
term 7xy and – 2 is the numerical coefficient of the term –2x. on. Also, the coefficient (–1) is
Sometimes, the word ‘coefficient’ is used in a more general way. indicated only by the minus sign.
Thus (–1) x is written as – x; (–1)
Thus, we say that in the term 7xy, 7 is the coefficient of xy, x x y is written as –x y and so on.
2 2
2 2
is the coefficient of 7y and y is the coefficient of 7x.
Thus, we can say a coefficient may be either a numerical factor or an algebraic factor or a product
of two or more factors. So, it is said to be the coefficient of the product of the remaining factors.

A constant term does not have any coefficient either numerical or algebraic coefficient.
For example: In the algebraic expression –3abc .
2
–3 is the numerical coefficient of abc .
2
2
a is the coefficient of the product of the remaining factor, i.e., –3bc .
2
b is the coefficient of the product of the remaining factor, i.e., –3ac .
c is the coefficient of the product of the remaining factor, i.e., –3ab.
2
Teacher’s Tell students of the class that in the tree diagram, we have used dotted lines for factors and continuous lines for
Tip terms. This is to avoid mixing them.

113 Introduction to Algebra