Page 125 - Maths Skills - 7

Algebraic Expressions 123

Let’s Attempt

Example 1: Add the following:

(i) – 3ab, 17ab, 13ab (ii) 2pq – 3c, 14c + 7pq, pq – 5c
Solution: (i) – 3ab, 17ab, 13ab (ii) 2pq – 3c, 14c + 7pq, pq – 5c
Since all are like terms, add the Using column method, write the like
numerical coefficients by using terms one below the other
linear method. 2pq – 3c  (27 1++ pq = 10pq 
)
(– 3 + 17 + 13)ab = 27ab 7pq + 14c  ( 3145−+ − ) =c 6c 


+ pq – 5c
10pq + 6c

Example 2: Simplify by combining the like terms:

(i) 2x + 3x + 2x – 4, x – 2x + 5x – 2, – 4x + x – 4x + 3
3
2
3
2
3
2
(ii) 3p – 4p + 2, – 5p + 8p + 7, – 6p + 7p – 5
2
2
2
Solution: (i) 2x + 3 + 2x – 4 (ii) 3p – 4p + 2 + (– 5p + 8p + 7) + (– 6p + 7p – 5)
2
3
2
2
2
x – 2x + 5x – 2 = 3p – 5p – 6p – 4p + 8p + 7p + 2 + 7 – 5
2
3
2
2
2
– 4x + x – 4x + 3 = – 8p + 11p + 4
2
3
2
– x + 2x + 3x – 3
3
2
Example 3: Subtract the following:
(i) 5p – 3 from 2p – 7 (ii) – 4k + 14 + 3k from –3k – 14k – 8
2
2
4
2
4
2
(iii) 13n + 11n – 2n from –13n – 3n – 6n 4
2
4
2
Solution: (i) (2p – 7) – (5p – 3) (ii) Column method
2
2
= 2p – 7 – 5p + 3 (Change the sign) – 3k – 14k – 8

2
2
4
2

= 2p – 5p – 7 + 3 (Combine the like terms) – 4k + 3k + 14
2
4
2
2
= – 3p – 4 + – – (Change the signs here)
2
k – 17k – 22
4
2
(iii) (– 13n – 3n – 6n ) – (13n + 11n – 2n ) Fact-o-meter
4
2
2
4
= – 13n – 3n – 6n – 13n – 11n + 2n 4 To subtract an algebraic expression
2
4
2
= (– 13 – 13)n + (– 3 – 11)n + (– 6 + 2)n 4 from another, change the sign
2
= – 26n – 14n – 4n 4 (from ‘+’ to ‘–’ and from ‘–’ to ‘+’) of
2
Example 4: Find the sum: each term of the expression to be
subtracted and then add.
(i) (2x + 4x – 8) + (x – 3)
2
2
(ii) (20x – 3x + 2x + x – 5) + (14x – 7x + 12x + 2x – 9)
4
2
4
3
2
3
Solution: (i) 2x + 4x – 8 + x – 3 (ii) 20x – 3x + 2x + x – 5 + 14x – 7x + 12x + 2x – 9
2
2
2
4
3
3
2
4
= 2x + x + 4x – 8 – 3 = 20x + 14x – 3x – 7x + 2x + 12x + x + 2x – 5 – 9
2
2
2
4
2
3
3
4
= 3x + 4x – 11 = 34x – 10x + 14x + 3x – 14
2
4
2
3