Page 95 - Start Up Mathematics_8 (Non CCE)

7
6
8
2 3
8
Example 10: Find the product: (a) –3a ¥ (–5a ) ¥ (–4a ) (b) -2 ab ¥ 1 ab ¥ Ê -3 ab ˆ ˜
7 5
Á
9 3 Ë 5 ¯
8
7
6
8
6
7
Solution: (a) –3a ¥ (–5a ) ¥ (–4a ) = {–3 ¥ (–5) ¥ (–4)} ¥ (a ¥ a ¥ a )
= –60 ¥ a 6 + 7 + 8 = –60a 21
- ˆ ¸
-2 1 Ê -3 ˆ Ï -2 1 Ê 3 8 2 7 3 5
8
7 5
2 3
(b) ab ¥ ab ¥ Á ab ˜ = Ì ¥¥ Á ˜ ˝ ¥ (a ¥ a ¥ a ) ¥ (b ¥ b ¥ b )
9 3 Ë 5 ¯ Ó 9 3 Ë 5 ¯ ˛
2 2
17 9
= ¥ a 8 + 2 + 7 ¥ b 1 + 3 + 5 = a b
45 45
Example 11: Express the following product as a monomial and verify the result for x = –1, y = 1, and z = 2.
2 xy z ¥ Ê - 9 x 2 ˆ ¥ 10 yz ¥ 04.
2
2
Ë
¯
3 Á 10 ˜ 27
2 Ê - 9 2 ˆ 10 Ï 2 Ê - 9ˆ 10 4 ¸
Solution: xy z ¥ Á x ˜ ¥ yz ¥ 04. = Ì ¥ Á ˜ ¥ ¥ ˝ ¥ (x ¥ x 2 ) ¥ (y 2 ¥ ) (y ¥ z ¥ z 2 )
2
2
3 Ë 10 ¯ 27 Ó 3 Ë 10 ¯ 27 10 ˛
-4 -4
3 3
+
= ¥ x 1 + 2 ¥ y 21 ¥ z 1 + 2 = x yz
3
45 45
To verify the result for x = –1, y = 1 and z = 2
2 Ê - 9 2 ˆ 10
2
2
LHS = xy z ¥ Á x ˜ ¥ yz ¥ 04.
3 Ë 10 ¯ 27
{ 2 } { - 9 } { 10 }
= 3 ¥-() 1 ¥ 2 ¥ 10 ¥-() 2 ¥ 27 ¥ 1¥ () 2 ¥ 04.
2
2
1
1 ¥ ()
2 Ê - ˆ 9 10
= ¥ (–1) ¥ 1 ¥ 2 ¥ Á ˜ ¥ 1 ¥ ¥ 1 ¥ 4 ¥ 0.4
3 Ë 10 ¯ 27
-2 -9 10 4 64 32
= ¥¥2 ¥ ¥ ¥4 = =
3 10 27 10 90 45
-4 3 3 3 -4 3 3 3 -4 32
RHS = x y z = ¥ (–1) ¥ (1) ¥ (2) = ¥ (–1) ¥ 8 =
45 45 45 45
\ LHS = RHS
Hence verified.
EXERCISE 5.3

1. Find the following products:

2
8
6
2
2
(a) 5z ¥ (–3z ) (b) –6x yz ¥ 2 xy 3 (c) -8 xyz 3 ¥ Ê Á -3 xyz ˆ ˜
5 5 Ë 4 ¯
16 9 3 2 50 2 2 Ê -12 ˆ -6 3
4 2
3
24
2
(d) pqr ¥ p q r (e) a b ¥ Á abc (f) lm n ¥ l mn
˜
9 8 3 Ë 25 ¯ 7 5
87