Page 139 - ICSE Math 6

12 Operations on Algebraic

Expressions

Key Concepts

• Addition, Subtraction and Multiplication of Algebraic • Evaluation of Algebraic Expressions by Substituting
Expressions a Value for the Variable
• Use of Brackets as Grouping Symbols

In the previous chapter, we learnt about algebraic expressions. In this chapter, we will learn to apply
mathematical operations on algebraic expressions and find their values by substituting the values of
the variables.

Addition

Addition of like terms
The sum of two or more like terms is a term whose numerical coefficient is the sum of the numerical
coefficients of the given terms. For example,
(a) 3a + 6a = (3 + 6)a = 9a Maths Info

2
2
2
(b) 5p + 15p = (5 + 15)p = 20p 2
Like terms along with their sum
+ +
5  5   4 6 5  15 form a group of like terms.
(c) 2xy + 3xy + xy =  2 3 xy =   xy = xy
++ 
2  2   2  2
Addition of unlike terms
Two unlike terms can never be added together to get a single term. So, we just write the unlike terms
as the terms of the algebraic expression with an addition sign. For example, the sum of 2ab and 3xy
is 2ab + 3xy.

Example 1: Add the following.
2
2
(a) 2xy and –13xy (b) 5pq and 6pq (c) 3 y and 3yz
− 3
2
2
(d) –15pa and pa (e) 2ab, –8ab and –7ab (f) –3x , –4y , 5x 2
5
Solution: (a) 2xy + (–13xy) = 2xy – 13xy = (2 – 13)xy = –11xy
(b) 5pq + 6pq = (5 + 6)pq = 11pq

2

2
(c) Since, y and 3yz are unlike terms, they cannot be added to get a single term.
3
2 2
2
2
\ Sum of y and 3yz = y + 3yz
3 3
 –3   3   –75 – 3  –78
(d) (–15pa) +  pa = –15 –  pa =   pa = pa


 5   5   5  5
(e) 2ab + (–8ab) + (–7ab) = (2 – 8 – 7)ab = –13ab
2
2
2
2
2
2
(f) (–3x ) + (–4y ) + 5x = (–3 + 5)x – 4y = 2x – 4y 2
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