Page 78 - Maths Skills - 8

76 Maths

Example 2: Find the value of (5x y) × (– 4xy ), when x = 2 and y = – 5.
2
2
Solution: (5x y) × (– 4xy ) = {5 × 2 × (– 5)} × {(– 4) × 2 × (– 5) }
2
2
2
2
= (– 100) × (– 200) = 20000
Example 3: Multiply − 7 xy by 10 xy and verify your result for x = 1 and y = 3.
3
3
9 11
 7  10 
Solution: We have,  − xy  ×  xy 3 
3
 9   11 
7 10
= × (x × x × y × y ) = − 70 × x 3 + 1 × y 1 + 3 = − 70 x y
3
3
4 4

9 11 99 99
Verification: For x = 1 and y = 3
7

LHS = xy 10 xy 3 RHS = − 70 xy 4
3

4

9 11 99

7

= 1 3 3 10 13 = 70 1 4 3 = 70 81 = − 630
4
3

9 11 99 99 11
21
= 270 = − 630

9 11 11
Thus, LHS = RHS
Example 4: Find the product of 2x y and (3x + y ).
3
2
2
Solution: We have, 2x y × (3x + y ) = (2x y × 3x ) + (2x y × y ) = 6x y + 2x y
2 3
2
2
2
3
2
5
3
2

1
Example 5: Multiply 5x 2 x y 4 by xy and verify the result for x = 1 and y = 2.
2
3

3 3

2
2
2
5
Solution: 5x 2 x y 4 1 x y = 5x 1 x y 2 x y 1 x y = xy − 2 xy 5

5
3
3
3
4

3 3 3 3 3 3 9
Verification: For x = 1, y = 2

2
5
LHS = 5x 2 x y 4 1 x y and RHS = xy − 2 xy 5

5
3
3

3 3 3 9

5
= 51 2 1 2 4 1 1 2 = 1 2 1 2 = 10 − 64 = − 34

3
5
5
3
2

2

3 3 3 9 3 9 9
32 17 34
2
2

= 5 = = −

3 3 9
3
3
Thus, LHS = RHS
Exercise 5.2
1. Multiply the following.
(i) 11x y and 2x y (ii) 3y and 7y (iii) 5x and 4x (iv) – 9xy and 4x z
2
5
2
2 2
2
9
3