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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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