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Solution: Horizontal Method Column Method

(a) 2x − 3y from 4x + y Write the expressions one below
(4x + y) – (2x – 3y) = 4x + y − 2x + 3y the other with the like terms

( Changing sign + to – and – to +) appearing exactly below like
terms as:
= (4x − 2x) + (y + 3y) 4xy
+
= (4 − 2)x + (1 + 3)y 2x − 3y (Changing the sign
= 2x + 4y − + of each term)
2x + 4y

(b) Horizontal Method Column Method

2a − 3b − 5c from a + 4b + 7c a + 4 b + 7 c
(a + 4b + 7c) − (2a − 3b − 5c) 2 a − 3 b − 5 c (Changing the sign
− + +
= a + 4b + 7c – 2a + 3b + 5c −+ 7 b+ 12 c of each term)
a
( Changing sign + to – and – to +)
= (1 − 2)a + (4 + 3)b + (7 + 5)c

= –a + 7b + 12c

Example 22: Subtract 24pq – 10q – 18p from 30pq + 12q + 14p.
Solution: 30pq + 12q + 14p – (24pq – 10q – 18p) = 30pq + 12q + 14p – 24pq + 10q + 18p
= 30pq – 24pq + 12q + 10q + 14p + 18p

= 6pq + 22q + 32p
Example 23: Subtract the sum of 2p − q + 3r and p + 3q − r from 7p + 2q.

Solution: The sum of 2p – q + 3r and p + 3q – r is:
2pq−+ 3r
−
p + 3q r
3p + 2q+ 2r

Thus, the sum of (2p − q + 3r) and (p + 3q − r) is 3p + 2q + 2r.
Now, we have to subtract (3p + 2q + 2r) from (7p + 2q).
7p+ 2q
3p + 2q + 2r
−− −

4p − 2r

Hence, the required answer is 4p − 2r.
Example 24: The sum of two numbers is 2x − 3xy + 5y. If one of them is x + 2xy −3y, find the other.
Solution: Other number = (2x − 3xy + 5y) − (x + 2xy − 3y)

= 2x − 3xy + 5y − x − 2xy + 3y
= (2 − 1)x + (−3 − 2)xy + (5 + 3)y = x − 5xy + 8y

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