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Using the identity (a + b)(a – b) = a2 – b2, find the following product.

(i) (p + 2) (p – 2)

(ii) (1 + 3b) (3b – 1)

(iii) (4 – mn) (mn + 4)

(iv) (6x + 7y) (6x – 7y)

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(i) (p + 2) (p – 2)

Substituting a = p; b = 2 in the identity 

(a + b) (a – b) = a2 – b2, we get

(p + 2) (p – 2) = p2 – 22

(ii) (1 + 3b) (3b – 1)

(1 + 3b) (3b -1) can be written as (3b + 1) (3b – 1)

Substituting a = 36 and b = 1 in the identity

(a + b) (a – b) = a2 – b2, we get

(3b + 1) (3b – 1) = (3b)2 – 12 

= 32 x b2 – 12

(3b + 1) (3b – 1) = 9b2 – 12

(iii) (4 – mn) (mn + 4)

(4 – mn) (mn + 4) can be written as (4 – mn) (4 + mn) = (4 + mn) (4 – mn)

Substituting a = 4 and b = mn is

(a + b) (a – b) = a2 – b2, we get

(4 + mn) (4 – mn) = 42 – (mn)2 

= 16 – m2 n2

(iv) (6x + 7y) (6x – 7y)

Substituting a = 6x and b = 7y in

(a + b) (a – b) = a2 – b2, we get

(6x + 7y) (6x – 7y) = (6x)2 – (7y)2 

= 62x2 – 72y2

(6x + 7y) (6x – 7y) = (6x)2 – (7y)2 

= 62x2 – 72y2

(6x + 7y) (6x – 7y) = 36x2 – 49y2

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