CBSE Class 8CBSE
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Applying Identities

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For example : Using the Identity (I), find   `(2x + 3y)^2`
 `(2x + 3y)^2 = (2x)^2 + 2(2x) (3y) + (3y)^2`     [Using the Identity (I)] 
`= 4x^2 + 12xy + 9y^2`

For example : Using Identity (II), find `(4p – 3q)^2`
 `(4p – 3q)^2 =(4p)^2 – 2 (4p) (3q) + (3q)^2`   [Using the Identity (II)] 
`= 16p^2 – 24pq + 9q^2`

For example : Using Identity (III), find `(3/2 m + 2/3 n)(3/2m - 2/3 n)`
`(3/2 m + 2/3 n)(3/2m - 2/3 n)`

`= (3/2 m)^2 - (2/3 n)^2`

`= 9/4 m^2 - 4/9 n^2` 

For example :  Use the Identity (x + a) (x + b) = x2 + (a + b) x + ab to find the following: 
(i) 501 × 502  =  (500 + 1) × (500 + 2) 
= `500^2 + (1 + 2) × 500 + 1 × 2` 
= 250000 + 1500 + 2 = 251502  

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