Example 10. If abc 2 and abbcac 1 , what is the value of
(ab)^2 (bc)^2 (ca)^2?
Solution :(ab)^2 (bc)^2 (ca)^2
= a^2 2 abb^2 b^2 2 bcc^2 c^2 2 caa^2
= (a^2 b^2 c^2 2 ab 2 bc 2 ca)(a^2 b^2 c^2 )
= (abc)^2 {(abc)^2 2 (abbcac)}
= ( 2 )^2 ( 2 )^2 2 u 1
= 4 4 2 8 2 6
Example 11. Express ( 2 x 3 y)( 4 x 5 y) as the difference of two squares.
Solution : Let, 2 x 3 y a and 4 x 5 y b
? Given expression =
2 2
2 2
̧
¹̈ ·
©̧ §
¹̈ ·
©ab §ab a b=
2 2
22 3 4 5
22 3 4 5
̧
¹·
̈
©§
̧
¹·
̈
©§ x y x y x y x y [substituting the values of a and b]=
2 228 2
26 2
̧
¹̈ ·
©̧ §
¹̈ ·
©§ x y y x=
2 2
22 ( 4 )
22 ( 3 )
̧
¹·
̈
©§
̧
¹·
̈
©§ xy y x=( 3 xy)^2 ( 4 yx)^2
? ( 2 x 3 y)( 4 x 5 y) ( 3 xy)^2 ( 4 yx)^2
Activity : 1. Simplify :( 4 x 3 y)^2 2 ( 4 x 3 y)( 4 x 3 y)( 4 x 3 y)^2- If xyz 12 and x^2 y^2 z^2 50 , find the
value of (xy)^2 (yz)^2 (zx)^2.
Exercise 3⋅ 1- Find the square with the help of the formulae :
(a) 2 a 3 b (b) 2 ab 3 bc (c)^22
2
y
x (d)
aa
1
(e) 4 y 5 x (f) abc(g) 5 x^2 y (h) x 2 y 4 z (i) 3 p 4 q 5 r (j) 3 b 5 c 2 a (k) axbycz
(l)abcd (m) 2 a 3 x 2 y 5 z (n) 101 (o) 997 (p) 1007
- Simplify :
(a) ( 2 a 7 )^2 2 ( 2 a 7 )( 2 a 7 )( 2 a 7 )^2