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Addition of Algebraic Expressions

As we know that an algebraic expression may have like and unlike terms. In addition, we rearrange
the different like terms in groups and add them. We can add algebraic expressions using two
methods: Horizontal method and Column method.

Let us take some example to understand the concept.

Example 20: Add the following:

(a) ab + bc and bc + ca
(b) 3x − y + z, 2y − 5z and 3z − 4x
(c) 3p − q + 5r, q – 2r and 3r – 2p + 7q

Solution: Horizontal Method Column Method
(a) (ab + bc) + (bc + ca) = ab + (bc + bc) + ca Write the like terms one below

= ab + (1 + 1)bc + ca the other. ab+bc
= ab + 2bc + ca
+bc+ca

ab + 2 bc ca
+
(b) Horizontal Method Column Method
3xy−+ z
3x − y + z, 2y − 5z and 3z − 4x
2y − 5z
(3x − y + z) + (2y − 5z) + (3z − 4x) = (3x – 4x)
+ (–y + 2y) + (z – 5z + 3z) − 4x + 3z
x
−+ y − z
(Q Rearranging like terms)
= (3 – 4)x + (–1 + 2)y + (1 – 5 + 3)z
= –x + y – z

(c) Horizontal Method Column Method
q
3p − q + 5r, q – 2r and 3r – 2p + 7q 3p −+ 5r
(3p − q + 5r) + (q – 2r) + (3r – 2p + 7q) q − 2r
− 2p + 7q + 3r
(Q Rearranging like terms)
p + 7q + 6r
= (3p –2p) + (–q + q +7q) + (5r – 2r + 3r)
= p + 7q + 6r

Subtraction of Algebraic Expression

To subtract an algebraic expression from another expression, We change the sign of each term
of the expression which is to be subtracted as (+ to – and – to +) and add to the expression from
which the subtraction is to be made.

Let us take some examples to understand the concept.
Example 21: Subtract the following:

(a) 2x − 3y from 4x + y (b) 2a − 3b − 5c from a + 4b + 7c

119 Introduction to Algebra