= a^2 b^2 c^2 2 ab 2 bc 2 ac
Example 1. What is the square of ( 4 x 5 y)?
Solution :( 4 x 5 y)^2 ( 4 x)^2 2 u( 4 x)u( 5 y)( 5 y)^2
= 16 x^2 40 xy 25 y^2
Example 2. What is the square of ( 3 a 7 b)?
Solution :( 3 a 7 b)^2 ( 3 a)^2 2 u( 3 a)u( 7 b)( 7 b)^2
= 9 a^2 42 ab 49 b^2
Example 3. Find the square of 996 by applying the formula of square.
Solution :( 996 )^2 ( 1000 4 )^2
= ( 1000 )^2 2 u 1000 u 4 ( 4 )^2
= 1000000 8000 16
= 1000016 8000
= 992016
Example 4. What is the square of abcd?
Solution : (abcd)^2 {(ab)(cd)}^2
= (ab)^2 2 (ab)(cd)(cd)^2
= a^2 2 abb^2 2 (acadbcbd)c^2 2 cdd^2
= a^2 2 abb^2 2 ac 2 ad 2 bc 2 bdc^2 2 cdd^2
= a^2 b^2 c^2 d^2 2 ab 2 ac 2 ad 2 bc 2 bd 2 cd
Activity : Find the square with the help of the formulae :
- 3 xy 2 ax 2. 4 x 3 y 3. x 5 y 2 z
Example 5. Simplify :
( 5 x 7 y 3 z)^2 2 ( 7 x 7 y 3 z)( 5 x 7 y 3 z)( 7 x 7 y 3 z)^2Solution : Let, 5 x 7 y 3 z a and 7 x 7 y 3 z b
? Given expression = a^2 2 .b.ab^2
= a^2 2 abb^2
= (ab)^2
= {( 5 x 7 y 3 z)( 7 x 7 y 3 z)}^2
[substituting the values of a and b]=( 5 x 7 y 3 z 7 x 7 y 3 z)^2
= ( 12 x)^2
= 144 x^2